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
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