# Examples on Highest Common Factor (H.C.F)

Highest common factor is the highest or greatest number that divides the two or three numbers without leaving any remainder. So that highest number is called the H.C.F of that group of two or three numbers.

This topic will provide examples on H.C.F (highest common factor) which will help the learners to improve their knowledge, understanding and will help in getting a clear understanding of the concepts on H.C.F better.

**Here are few illustrated on Highest Common Factor (H. C.F)**

**1. Find the H.C.F of 75, 50 and 125**

**Solution:**

The factors of 75 are = 5 × 5 × 3 = 5^{2 }× 3

The factors of 50 are = 5 × 5 × 2 = 5^{2 }× 2

The factors of 125 are = 5 × 5 × 5 = 5^{3}

Therefore, the common prime factor of 75, 50 and 125 is 5

The lowest power of 5 is 5^{2}

Therefore, H.C.F = 5^{2 }= 5 × 5 = 25

**2. Find the H.C.F of 64, 32, and 256**

**Solution:**

The factors of 64 are = 2 × 2 × 2 × 2 × 2 × 2 = 2^{6}

The factors of 32 are = 2 × 2 × 2 × 2 × 2 = 2^{5}

The factors of 256 are = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{8}

Therefore, the common prime factor of 64, 32 and 256 is 2

The lowest power of 2 is 2^{5}

Therefore, H.C.F = 2 × 2 × 2 × 2 × 2 = 32

**3. Find the H.C.F of 11, 121, and 1331**

**Solution:**

The factor of 11 is = 11

The factors of 121 are = 11 × 11 =11^{2}

The factors of 1331 are = 11 × 11 × 11 = 11^{3}

Therefore, the common prime factor of 11, 121, and 1331 is 11

The lowest power of 11 is 11

Therefore, H.C.F = 11

**4. Find the H.C.F of 48, 96, and 12**

**Solution:**

The factors of 48 are = 2 × 2 × 2 × 2 × 3 = 2^{4} × 3

The factors of 96 are = 2 × 2 × 2 × 2 × 2 × 3 = 2^{5} × 3

The factors of 12 are = 2 × 2 × 3 = 2^{2} × 3

Therefore, the common prime factors of 48, 96 and 12 are 2 and 3

The lowest power of 2 is 2^{2}

The lowest power of 3 is 3

Therefore, H.C.F = 2 × 2 × 3 = 12

**5. Find the H.C.F of 81, 27 and 33**

**Solution:**

The factors of 81 are = 3 × 3 × 3 × 3 = 3^{4}

The factors of 27 are = 3 × 3 × 3 = 3^{3}

The factors of 33 are = 3 × 11

Therefore, the common prime factors of 81, 27 and 33 is 3

The lowest power of 3 is 3

Therefore, H.C.F = 3

## You might like these

This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110

Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is

**5th Grade Math**

**From Examples on Highest Common Factor (H.C.F) to HOME PAGE**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below.