H.C.F that is highest common factor is also called G.C.D i.e. Greatest Common Divisor is the greatest or highest number which exactly divides two or more numbers.
Steps to find out the H.C.F (Highest Common factor)
Step I: First find out the prime factors of each of the numbers
Step II: Then find out the common prime factor of those numbers
Step III: The product of lower power of common factors is the H. C. F
Here are few examples to illustrate H. C. F (Highest Common Factor)
1. Find the H.C.F of 27 and 36
Solution:
The factors of 27 = 3 × 3 × 3 = 3^{3}
The factors of 36 = 2 × 2 × 3 × 3 = 2^{2 }× 3^{2}
The common prime factor is 3
The lowest power of 3 is 3^{2}
Therefore, H. C. F = 3 × 3 = 9
2. Find the H.C.F of 24 and 12
Solution:
The factors of 24 = 2 × 2 × 2 × 3 = 2^{3} × 3
The factors of 12 = 2 × 2 × 3 = 2^{2} × 3
The common prime factors 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
3. Find the H.C.F of 25 and 50
Solution:
The factors of 25 = 5 × 5 = 5^{2}
The factors of 50 = 2 × 5 × 5 = 5^{2 }× 2
The common prime factor is 5
The lowest power of 5 is 5^{2}
Therefore, H. C. F = 5 × 5 = 25
4. Find the H.C.F of 18 and 36
Solution:
The factors of 18 = 2 × 3 × 3 = 2 × 3^{2}
The factors of 36 = 2 × 2 × 3 × 3 = 2^{2 }× 3^{2}
The common prime factors are 2 and 3
The lowest power of 3 is 3^{2}
The lowest power of 2 is 2
Therefore, H. C. F = 2 × 3 × 3 = 18
5. Find the H.C.F of 55 and 35
Solution:
The factors of 55 = 5 × 11
The factors of 36 = 5 × 7
The common prime factors is 5
The lowest power of 5 is 5
Therefore, H. C. F = 5
6.Find the H.C.F of 12, 18 and 15
Solution:
The factors of 12 = 2 × 2 × 3 = 2^{2} × 3
The factors of 18 = 2 × 3 × 3 = 2 × 3^{2}
The factors of 15 = 3 × 5
The common prime factor is 3
The lowest power of 3 is 3
Therefore, H. C. F = 3
7. Find the H.C.F of 48 and 60
Solution:
The factors of 48 = 2 × 2 × 2 × 2 × 3 = 2^{4} × 3
The factors of 60 = 5 × 2 × 2 × 3 = 5 × 2^{2} ×3
The common prime factors 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
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