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Even & Odd Numbers – Class 1 & 2 Maths | CBSE & UP Board | GPN

Class 1 Class 2 CBSE UP Board

📘 What's inside:

Concept 1 — What are Even Numbers?

Let us observe what happens when we arrange objects in pairs of two.

When we can arrange a group of objects into exact pairs with nothing left over, the count is called an even number.

2 — Even
4 — Even
6 — Even
8 — Even
▶ Even Numbers Rule
  • An even number can be divided into two equal groups with nothing left over.
  • Even numbers always end in 0, 2, 4, 6 or 8.
  • The first ten even numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
  • 0 is also considered an even number.
▶ Solved Example 1
Meena has 8 pencils. She arranges them in pairs. Does she have an even number of pencils?
  1. 1Arrange 8 pencils into pairs: (2), (2), (2), (2). That is 4 complete pairs.
  2. 2No pencil is left over. Every pencil has a partner.
  3. 3Also check the ones digit: 8 ends in 8. 8 is in the list 0, 2, 4, 6, 8. So 8 is even.
Yes, 8 is an even number. Meena can arrange all pencils in perfect pairs.
▶ Solved Example 2
Write all even numbers from 1 to 20.
  1. 1Check each number from 1 to 20. Even numbers end in 0, 2, 4, 6 or 8.
  2. 22 → ends in 2 → even.   4 → even.   6 → even.   8 → even.   10 → ends in 0 → even.
  3. 312, 14, 16, 18, 20 — all even (ends in 2, 4, 6, 8, 0).
Even Numbers (1 to 20)
2468101214161820
Even numbers from 1 to 20: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

✍ Practice — Concept 1

Q1 Which of these are even numbers?   3, 6, 9, 12, 15, 18 ▼
Answer Check the ones digit of each:
3 → ends in 3 → not even
6 → ends in 6 → even
9 → ends in 9 → not even
12 → ends in 2 → even
15 → ends in 5 → not even
18 → ends in 8 → even
Even numbers: 6, 12, 18
Q2 A bag has 14 sweets. Can they be shared equally between 2 friends with none left over? How do you know? ▼
Answer 14 ends in 4. 4 is in the list 0, 2, 4, 6, 8. So 14 is an even number.
Even numbers can always be split into 2 equal groups.
Yes, each friend gets 7 sweets with none left over.
Q3 Write the next three even numbers after 16. ▼
Answer Even numbers increase by 2 each time.
16 + 2 = 18
18 + 2 = 20
20 + 2 = 22
Next three even numbers: 18, 20, 22
Q4 True or False: 0 is an even number. ▼
Answer True.
0 ends in 0. 0 is in the list of even endings (0, 2, 4, 6, 8).
Also, 0 objects can be arranged into 0 pairs with nothing left over.
0 is an even number.

Concept 2 — What are Odd Numbers?

When we arrange objects in pairs and one object is always left over, the count is called an odd number.

1 — Odd
3 — Odd
5 — Odd
7 — Odd
▶ Odd Numbers Rule
  • An odd number cannot be divided into two equal groups — one is always left over.
  • Odd numbers always end in 1, 3, 5, 7 or 9.
  • The first ten odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
⚠ Remember

Every number is either even or odd — never both. There is no number that is neither even nor odd. This is true for every counting number.

▶ Solved Example 3
Raju has 9 marbles. He tries to divide them equally between himself and his brother. Can he do it? Is 9 even or odd?
  1. 1Try arranging 9 marbles in pairs: (2), (2), (2), (2) — that is 4 pairs with 1 marble left over.
  2. 2There is a leftover. So 9 is an odd number.
  3. 3Check ones digit: 9 ends in 9. 9 is in the list 1, 3, 5, 7, 9. Confirmed — odd.
9 is an odd number. Raju cannot share equally — one marble will always be left over.
▶ Solved Example 4
Write all odd numbers from 1 to 20.
  1. 1Check ones digit of each number from 1 to 20. Odd ends in 1, 3, 5, 7 or 9.
  2. 21, 3, 5, 7, 9 → all odd.
  3. 311, 13, 15, 17, 19 → all odd (ends in 1, 3, 5, 7, 9).
Odd Numbers (1 to 20)
135791113151719
Odd numbers from 1 to 20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

✍ Practice — Concept 2

Q5 Which of these are odd numbers?   4, 7, 10, 13, 16, 19 ▼
Answer 4 → ends in 4 → even
7 → ends in 7 → odd
10 → ends in 0 → even
13 → ends in 3 → odd
16 → ends in 6 → even
19 → ends in 9 → odd
Odd numbers: 7, 13, 19
Q6 Write the next three odd numbers after 11. ▼
Answer Odd numbers increase by 2 each time.
11 + 2 = 13
13 + 2 = 15
15 + 2 = 17
Next three odd numbers: 13, 15, 17
Q7 A teacher has 17 chocolates to give equally to two groups. Will there be any left over? Why? ▼
Answer 17 ends in 7. 7 is in the odd digits list (1, 3, 5, 7, 9). So 17 is an odd number.
Odd numbers cannot be split into 2 equal groups.
Yes, 1 chocolate will be left over. (Each group gets 8, one remains.)
» Deepen your understanding with Writing Numbers Using Place Value Blocks and practice using the Free Worksheet. You can also explore Comparing Numbers (Greater Than/Less Than) and reinforce your skills with its accompanying worksheet.

Concept 3 — The Ones Digit Rule

We do not need to count pairs every time. There is a much faster rule: just look at the ones digit.

Even — Ones digit is
0 2 4 6 8
Odd — Ones digit is
1 3 5 7 9
▶ How to Apply the Rule
  • Look at the last digit (ones digit) of the number only.
  • If last digit is 0, 2, 4, 6 or 8 → the number is even.
  • If last digit is 1, 3, 5, 7 or 9 → the number is odd.
  • The tens, hundreds or thousands digits do not matter at all.

Tap each number to find out if it is even or odd:

Cyan = Even    Gold = Odd
▶ Solved Example 5
Is 764 even or odd? Is 835 even or odd?
  1. 1764 → Ones digit = 4. 4 is in the even list (0,2,4,6,8). So 764 is even.
  2. 2835 → Ones digit = 5. 5 is in the odd list (1,3,5,7,9). So 835 is odd.
  3. 3We only looked at the last digit — the hundreds and tens digits (7, 6 and 8, 3) did not matter at all.
764 is even (ones digit = 4)    835 is odd (ones digit = 5)
▶ Solved Example 6
A student says “372 is odd because 3 + 7 + 2 = 12 and 12 is even — wait, I am confused.” Help the student. Is 372 even or odd?
  1. 1We do not add the digits to find even or odd. That is a rule for divisibility by 3 — a different topic.
  2. 2To find even or odd, look at the ones digit only.
  3. 3372 → Ones digit = 2. 2 is in the even list. So 372 is even.
372 is even. Only the ones digit (2) matters. Never add the digits to decide even or odd.

✍ Practice — Concept 3

Q8 Write E (even) or O (odd) for each:   25, 48, 63, 90, 77, 104 ▼
Answer 25 → ones digit 5 → O (odd)
48 → ones digit 8 → E (even)
63 → ones digit 3 → O (odd)
90 → ones digit 0 → E (even)
77 → ones digit 7 → O (odd)
104 → ones digit 4 → E (even)
Q9 Is 999 even or odd? Explain using the ones digit rule. ▼
Answer 999 → Ones digit = 9.
9 is in the odd list (1, 3, 5, 7, 9).
999 is an odd number.
Q10 Which digit in the ones place makes any number even? List all five. ▼
Answer A number is even if its ones digit is:
0, 2, 4, 6 or 8
These are the five even digits. Any number ending in one of these is always even.

Concept 4 — Sorting Even and Odd Numbers

Let us practise sorting a mixed group of numbers into even and odd. We use the ones digit rule for each number, then place it in the correct group.

▶ Solved Example 7
Sort these numbers into even and odd:
3, 8, 15, 22, 37, 40, 51, 64, 79, 86
  1. 1Check ones digit of each number.
  2. 2Even (0,2,4,6,8): 8 →8, 22 →2, 40 →0, 64 →4, 86 →6.
  3. 3Odd (1,3,5,7,9): 3 →3, 15 →5, 37 →7, 51 →1, 79 →9.
Even Numbers
8 22 40 64 86
Odd Numbers
3 15 37 51 79
Even: 8, 22, 40, 64, 86
Odd: 3, 15, 37, 51, 79
▶ Solved Example 8
In a class, there are 13 boys and 16 girls. Is the number of boys even or odd? Is the number of girls even or odd?
  1. 1Boys = 13. Ones digit = 3. 3 is odd. So 13 is odd.
  2. 2Girls = 16. Ones digit = 6. 6 is even. So 16 is even.
  3. 3The boys cannot be arranged in complete pairs (1 is left over). The girls can be arranged in complete pairs.
Number of boys (13) is odd.   Number of girls (16) is even.

✍ Practice — Concept 4

Q11 Sort into even and odd:   11, 24, 35, 48, 57, 62, 73, 86, 99, 100 ▼
Answer
Even
24486286100
Odd
1135577399
Q12 A shopkeeper has 47 apples, 32 oranges and 15 bananas. Which fruits have an even count? Which have an odd count? ▼
Answer 47 → ones digit 7 → odd (apples)
32 → ones digit 2 → even (oranges)
15 → ones digit 5 → odd (bananas)
Even count: Oranges (32)
Odd count: Apples (47) and Bananas (15)
Q13 How many even numbers are there from 1 to 20? How many odd numbers? ▼
Answer Even numbers from 1–20: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 → 10 numbers
Odd numbers from 1–20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 → 10 numbers
There are exactly 10 even and 10 odd numbers from 1 to 20.
In any range of 20 consecutive numbers, even and odd are always equal in count.
» Strengthen your English grammar with Collective and Abstract Nouns and test yourself using the Free Practice Worksheet. Next, master Noun – Gender, Number & Case with its dedicated worksheet. » हिंदी व्याकरण में भाववाचक संज्ञा – परिभाषा और भेद पढ़ें और अभ्यास वर्कशीट से अभ्यास करें, साथ ही संज्ञा के लिंग – परिभाषा और प्रकार को समझें और वर्कशीट से अभ्यास करें।

Concept 5 — Even and Odd Numbers up to 100

Let us observe the pattern of even and odd numbers across 1 to 100. Notice how they perfectly alternate — even, odd, even, odd — throughout.

Even numbers
Odd numbers
▶ Key Patterns to Notice
  • Even and odd numbers alternate perfectly: 1(odd), 2(even), 3(odd), 4(even) …
  • From 1 to 100, there are exactly 50 even and 50 odd numbers.
  • Every row of 10 has 5 even and 5 odd numbers.
  • The number after any even number is always odd, and vice versa.
▶ Solved Example 9
How many even numbers are there from 1 to 50? How many odd?
  1. 1From 1 to 50, even numbers are: 2, 4, 6 … 50. These are 50 ÷ 2 = 25 even numbers.
  2. 2Odd numbers are: 1, 3, 5 … 49. These are also 25 odd numbers.
  3. 3In any range of 50 consecutive numbers starting from 1, there are always exactly equal even and odd numbers.
From 1 to 50: 25 even numbers and 25 odd numbers.
▶ Solved Example 10
What comes just after 98? Is it even or odd? What comes just before 71? Is it even or odd?
  1. 1Just after 98 = 99. Ones digit = 9 → odd.
  2. 298 is even. The number after any even number is always odd. So 99 must be odd. Confirmed.
  3. 3Just before 71 = 70. Ones digit = 0 → even.
  4. 471 is odd. The number before any odd number is always even. So 70 must be even. Confirmed.
After 98 = 99 (odd)    Before 71 = 70 (even)

✍ Practice — Concept 5

Q14 Write all even numbers from 51 to 60. ▼
Answer Check ones digits from 51 to 60:
52 (2), 54 (4), 56 (6), 58 (8), 60 (0) → all even.
Even numbers from 51 to 60: 52, 54, 56, 58, 60
Q15 The number just before an even number is always ___. The number just after an odd number is always ___. ▼
Answer The number just before an even number is always odd.
(Example: before 10 is 9 — odd. Before 4 is 3 — odd.)

The number just after an odd number is always even.
(Example: after 7 is 8 — even. After 13 is 14 — even.)
Q16 From 81 to 90, how many numbers are odd? List them. ▼
Answer Check ones digits from 81 to 90:
81(1), 83(3), 85(5), 87(7), 89(9) → all odd.
5 odd numbers: 81, 83, 85, 87, 89
★ Key Points to Remember
  • A number that can be split into exact pairs is called even.
  • A number that has one left over when paired is called odd.
  • Even numbers end in 0, 2, 4, 6 or 8.
  • Odd numbers end in 1, 3, 5, 7 or 9.
  • Only look at the ones digit — tens and hundreds digits do not matter.
  • Even and odd numbers alternate — the number after any even is odd, and vice versa.
  • From 1 to 100, there are exactly 50 even and 50 odd numbers.

Exam Style — Full Topic

5 Questions on Even & Odd Numbers

Q1 Write E (even) or O (odd):   16, 29, 43, 58, 75, 80, 91, 100 ▼
Answer 16 → 6 → E    29 → 9 → O    43 → 3 → O    58 → 8 → E
75 → 5 → O    80 → 0 → E    91 → 1 → O    100 → 0 → E
Q2 Sort these numbers into even and odd groups: 5, 18, 23, 36, 41, 54, 67, 72 ▼
Answer
Even
18365472
Odd
5234167
Q3 A student writes: “All numbers ending in 5 are even because 5 is in the middle.” Is this correct? Explain. ▼
Answer No, this is completely wrong.
Numbers ending in 5 are odd, not even.
5 is in the odd list (1, 3, 5, 7, 9).
Examples: 5, 15, 25, 35, 45 — all are odd numbers.
Even numbers end in 0, 2, 4, 6 or 8 only.
Q4 Rohan has 24 stickers. Priya has 31 stickers. Who can share their stickers equally between 2 friends with none left over? Who cannot? ▼
Answer Rohan: 24 → ones digit 4 → even. Can be split equally. Each friend gets 12.
Priya: 31 → ones digit 1 → odd. Cannot be split equally. 1 sticker left over.
Rohan can share equally. Priya cannot.
Q5 Fill in the blanks:   (a) The even number just before 50 is ___.   (b) The odd number just after 88 is ___.   (c) How many odd numbers are there from 1 to 10? ▼
Answer (a) The even number just before 50 = 50 − 2 = 48.
(b) The odd number just after 88 = 88 + 1 = 89. Ones digit 9 → odd. Answer = 89.
(c) Odd numbers from 1 to 10: 1, 3, 5, 7, 9 = 5 odd numbers.
📄 Free Worksheet

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► Open Free Worksheet
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