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Find the GCF of 75, 100, and 175.

20
25
5
75

1 answer

To find the greatest common factor (GCF) of 75, 100, and 175, we can start by determining the prime factorization of each number.

  1. Prime factorization of 75:

    • 75 = 3 × 5²

  2. Prime factorization of 100:

    • 100 = 2² × 5²

  3. Prime factorization of 175:

    • 175 = 5² × 7

Now, we will find the common prime factors and their lowest powers in each factorization:

  • The only common prime factor is 5.
  • The lowest power of 5 that appears in all three factorizations is \(5²\).

Thus, the GCF is \(5² = 25\).

Hence, the GCF of 75, 100, and 175 is 25.