H. C. F that is highest common factor is also called Greatest Common Factor (G.C.F). There is actually no difference between the two. Greatest Common Factor is actually the greatest factor of two or more numbers.
Here are few examples on Greatest Common Factor
1. Find the greatest common factor of 56 and 63
Solution:
The prime factors of 56 are: 2 × 2 × 2 × 7 = 2^{3}×7
The prime factors of 63 are: 3 × 3 × 7 = 3^{2}× 7
The common prime factor of 56 and 63 is 7
The lowest power of 7 is 7
Therefore, G .C.F = 7
2. Find the greatest common factor of 42 and 44
Solution:
The prime factors of 42 are: 2 × 3 × 7
The prime factors of 44 are: 2 × 2 × 11 = 2^{2 }× 11
The common prime factor of 42 and 44 is 2
The lowest power of 2 is 2
Hence, G. C. F = 2
3. Find the greatest common factor of 88 and 110
Solution:
The prime factors of 88 are: 2 × 2 × 2 × 11 = 2^{3 }× 11
The prime factors of 110 are: 2 × 5 × 11
The common prime factors of 8 and 110 are 2 and 11
The lowest power of 2 is 2
The lowest power of 11 is 11
Hence, G. C. F = 2 × 11 = 22
4. Find the greatest common factor of 450 and 500
Solution:
The prime factors of 450 are: 2 × 5 × 5 × 3 × 3 = 2 × 5^{2 }× 3^{2}
The prime factors of 500 are: 2 × 2 × 5 × 5 × 5 = 2^{2} × 5^{3}
The common prime factors of 450 and 500 are 2 and 5
The lowest power of 2 is 2
The lowest power of 5 is 5^{2}
Therefore, G. C. F = 2 × 5^{2 }=2 ×5 ×5=50
5. Find the greatest common factor of 18 and 20
Solution:
The prime factors of 18 are: 2 × 3 × 3 = 2 × 3^{2}
The prime factors of 20 are: 2 × 2 × 5 = 2^{2 }× 5
The common prime factor of 18 and 20 is 2
The lowest power of 2 is 2
Therefore, G. C. F = 2
6. Find the greatest common factor of 35, 28 and 70
Solution:
The prime factors of 35 are: 5 ×7
The prime factors of 28 are: 2 × 2 × 7 = 2^{2 }×7
The prime factors of 70 = 2 × 5 × 7
The common prime factor of 35, 28 and 70 is
The lowest power of 7 is 7
Therefore, G. C. F = 7
7. Find the greatest common factor of 56, 28 and 128
Solution:
The prime factors of 56 are: 2 × 2 × 2 × 7 = 2^{3 }× 7
The prime factors of 28 are: 2 × 2 × 7 = 2^{2 }× 7
The prime factors of 128 are: 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{7}
The common prime factor of 56, 28 and 128 is 2
The lowest power of 2 is 2^{2}
Therefore, G. C. F = 2 × 2 = 4
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