Highest Common Factor can be found using several methods such as the cake and ladder method, long division method, factorization etc. We have covered different model questions in the HCF Worksheet for better practice. You just need to solve HCF Problems available in the Highest Common Factor Worksheet with Answers and test your conceptual knowledge. Attempt the HCF Questions existing here on a frequent basis and enhance your speed and accuracy.

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## Worksheet on HCF with Solutions

**Example 1:**

Find the common factors of the following examples and determine the HCF?

(i) 2 and 4

(ii) 3 and 9

(iii)16 and 20

(iv) 20 and 30

(v) 10 and 15

**Solution:**

(i) factors of 2 are 1,2

factors of 4 are 1,2,4

Common factors of 2 and 4 are 1,2.

HCF of 2,4 is 2.

(ii) factors of 3 are 1,3

factors of 9 are 1,3,9

Common factors of 3 and 9 are 1,3.

HCF of 3,9 is 3.

(iii)factors of 16 are 1,2,4,8,16

factors of 20 are 1,2,4,5,10,20

Common factors of 3 and 9 are 1,2,4.

HCF of 16,20 is 4.

(iv) factors of 20 are 1,2,4,5,10,20

factors of 30 are 1,2,3,5,6,10,15 and 30

Common factors of 20 and 30 are 1,2,5,10.

HCF of 20,30 is 10.

(v) factors of 10 are 1,2,5,10

factors of 15 are 1,3,5 and 15

Common factors of 20 and 30 are 1,5.

HCF of 10,15 is 5.

**Example 2. **

Find the common factors and the highest common factors of the given numbers?

(i)18 and 24

(ii) 9 and 27

**Solution:**

(i) factors of 18 are 1,2,3,6,9,18

factors of 24 are 1,2,3,4,6,8,12,24

common factors of 18 and 24 are 1,2,3,6.

The greatest common factor of 18 and 24 is 6.

(ii) factors of 9 are 1,3,9.

factors of 27 are 1,3,9,27.

common factors of 9 and 27 are 1,3,9.

The greatest common factor of 9 and 27 is 9.

**Example 3.
**Find the Highest Common Factor of the following examples using the Common Factors Method?

(i)12 and 21

(ii) 40 and 50

(iii) 60 and 80

**Solution:**

(i) factors of 12 are 1,2,3,4,6,12.

factors of 21 are 1,3,7,21.

common factors of 12 and 21 are 1,3 .

greatest common factors of 12 and 21 is 3.

(ii) factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.

factors of 50 are 1,2,5,10,25,50.

common factors of 40 and 50 are 1,2,5,10.

greatest common factors of 40 and 50 is 10.

(iii) factors of 60 are 1,2,3, 4, 5,6,10,12,15,20,30,60.

factors of 80 are 1,2,4,5,8,10,16,20,40,80.

common factors of 40 and 50 are 1,2,4,5,10,20.

greatest common factors of 40 and 50 is 20.

**Example 4.**

Evaluate the H.C.F using Prime Factors Method?

(i) 19 and 30

(ii) 16 and 32

(iii) 40 and 56

**Solution:**

(i) 19 and 30

Prime factors of 19 are 1 ×19.

Prime factors of 30 are 1× 2 ×3 ×5.

H.C.F of 18,30 is 1.

(ii) 16 and 32

Prime factors of 16 are 1 × 2 × 2 × 2 × 2.

Prime factors of 32 are 1× 2 ×2 ×2 × 2 × 2.

H.C.F of 16,32 is 16.

(iii) 40 and 56

Prime factors of 40 are 2 × 2 × 2 × 5.

Prime factors of 56 are 2 × 2 ×2 × 7.

H.C.F of 40,56 is 8.

**Example 5.
**Find H.C.F by Long Division method?

(i) 36 and 75

**Solution:**

Divide the largest number by the smallest number. Here 75 is the largest number and 36 is the smallest number.

Take the divisor as a new dividend and the remainder as the new divisor. Proceed till the remainder is zero and the last divisor is the H.C.F.

Divide 36 with 3. The remainder is zero. So the HCF is 3.

Hence 3 is the HCF of 36 and 75.

**Example 6:
**Find HCF of 40, 180 by long division method?

**Solution:**

Divide the largest number by the smallest number. Here 180 is the largest number and 40 is the smallest number.

Take the divisor as a new dividend and the remainder as the new divisor. Proceed till the remainder is zero and the last divisor is the H.C.F.

Divide 40 with 20. The remainder is zero. So the HCF is 20.

Hence, the HDF of 40,180 is 20.