Worksheet Class 4 Factors and Multiples | PDF - Free Printable

Here is the complete solution to the worksheet, with explanations for each answer.

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Section-A

Q.I True or False

1. One is a multiple of all the numbers. → False

*Explanation:* A multiple of a number is the product of that number and an integer. For example, multiples of 5 are 5, 10, 15, 20... One (1) is not a multiple of any number except 1 itself. In fact, 1 is a *factor* of all numbers, not a multiple.

2. A factor of a number is always greater than the number. → False

*Explanation:* Factors are numbers that divide another number exactly. For example, factors of 12 are 1, 2, 3, 4, 6, 12 — all of which are ≤ 12. The largest factor of any number is the number itself. So, factors are usually less than or equal to the number.

3. All prime numbers are odd. → False

*Explanation:* The number 2 is a prime number (it has exactly two distinct positive divisors: 1 and itself), but it is even. So, not all primes are odd. 2 is the only even prime number.

4. All even numbers have only even factors. → False

*Explanation:* Consider the even number 6. Its factors are 1, 2, 3, 6. Here, 1 and 3 are odd factors. So, even numbers can have odd factors too.

5. 63 ÷ 9 = 7, so 63 is a multiple of 9. → True

*Explanation:* If a number divides another number exactly (with no remainder), then the dividend is a multiple of the divisor. Since 63 ÷ 9 = 7 (exact division), 63 is indeed a multiple of 9.

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Q.II Fill in the blanks

1. ______ is a unique number. → 1

*Explanation:* The number 1 is unique because:
- It is neither prime nor composite.
- It is the multiplicative identity (any number × 1 = itself).
- It is the only natural number with exactly one positive divisor.

2. ______ is a smallest odd prime number. → 3

*Explanation:* Prime numbers are numbers >1 with exactly two distinct positive divisors. The smallest prime is 2 (even). The next prime is 3, which is odd. So, 3 is the smallest *odd* prime.

3. ______ and ______ are prime numbers between 8 and 14. → 11 and 13

*Explanation:* Numbers between 8 and 14: 9, 10, 11, 12, 13.
- 9 = 3×3 → not prime
- 10 = 2×5 → not prime
- 11 → prime
- 12 = 2×6 → not prime
- 13 → prime
So, 11 and 13 are the primes in this range.

4. The next two multiples of 20, 40, 60, ______, ______. → 80, 100

*Explanation:* These are multiples of 20: 20×1=20, 20×2=40, 20×3=60, so next are 20×4=80 and 20×5=100.

5. The HCF of two co-prime numbers is always ______. → 1

*Explanation:* Co-prime numbers are numbers that have no common factor other than 1. So, their Highest Common Factor (HCF) is always 1.

6. The difference between the two prime numbers is 2. They are called ______. → Twin primes

*Explanation:* Twin primes are pairs of prime numbers that differ by 2. Examples: (3,5), (5,7), (11,13), etc.

7. The first two common multiples of 6 and 8 are ______. → 24, 48

*Explanation:*
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54...
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56...
- Common multiples: 24, 48, 72...
So, the first two are 24 and 48.

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✔ Final Answers Summary:

Q.I True or False
1. False
2. False
3. False
4. False
5. True

Q.II Fill in the blanks
1. 1
2. 3
3. 11 and 13
4. 80, 100
5. 1
6. Twin primes
7. 24, 48

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