What is HCF (GCF)?
Highest Common Factor (H.C.F.) aka Greatest Common Factor (G.C.F.)
H.C.F (G.C.F)
The factors which are common to two or more numbers are called their common factors.
The factor which is greatest among the common factors of a given set of numbers is called their Highest Common Factor (H.C.F) or (G.C.F).
Example- Let us take two numbers 24 and 26 and find their H.C.F (G.C.F.).
Factors of 24- 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36- 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12
Greatest among all common factors is 12.
Thus, H.C.F. (G.C.F.) of 24 and 36 = 12
HCF by Prime Factorization Method
In this method, we express the given set of numbers as a product of their prime factors.
Then we find the common prime factors of the given numbers.
Finally, we find the H.C.F. (G.C.F.) of the numbers by multiplying their common factors.
Example-
Find the HCF of 18 and 24.
Let us find the prime factorization of 18 and 24 first.
Therefore, 18 = 2 x 3 x 3
And 24 = 2 x 2 x 2 x 3
We observe that, the
Common Prime Factors = 2 and 3
HCF of 18 and 24 = Product of Common Prime Factors
= 2 × 3 = 6
Thus, HCF (18 and 24) = 6
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