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Determine the Highest Common Factor (HCF) of each of the following:

A. 125 ; 325
Hcf =?
=?

Write the hcf in full

1 answer

To determine the Highest Common Factor (HCF) of 125 and 325, we can use the method of prime factorization.

  1. Prime factorization of 125:

    • 125 = 5 × 25
    • 25 = 5 × 5
    • Therefore, 125 = 5 × 5 × 5 = \(5^3\).

  2. Prime factorization of 325:

    • 325 = 5 × 65
    • 65 = 5 × 13
    • Therefore, 325 = 5 × 5 × 13 = \(5^2 × 13\).

  3. Identify the common prime factors:

    • The prime factor common to both numbers is 5.
    • The lowest power of 5 in both factorizations is \(5^2\) (which is for 325).

  4. Finding the HCF:

    • The HCF is \(5^2\) = 25.

So, the Highest Common Factor (HCF) of 125 and 325 is:

HCF = 25.