High School

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Pair A

Pair B

52,72 96, 64

Pair C

48,84

Select all the correct statements

about these pairs.

A Pair A and Pair C have the same GCF.

B All three pairs have GCFs that are

not prime numbers.

The GCF of Pair C is 12.

The GCF of Pair B is 16.

The prime factorization of the

GCF of Pair B is 2x2x2x2.

Pair A Pair B 52 72 96 64 Pair C 48 84 Select all the correct statements about these pairs A Pair A and Pair

Answer :

The correct statements about these pairs is The GCF of Pair C is 12. (option c).

Pair A:

The given pair A is (52, 72). To find the GCF of these numbers, we can factor them into their prime factors. The prime factorization of 52 is 2 x 2 x 13, and the prime factorization of 72 is 2 x 2 x 2 x 3 x 3. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 = 4. Therefore, the GCF of Pair A is 4.

Pair C:

The given pair C is (48, 84). Again, we can factor these numbers into their prime factors. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and the prime factorization of 84 is 2 x 2 x 3 x 7. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 x 3 = 12. Therefore, the GCF of Pair C is 12.

Pair B:

The given pair B is (96, 64). We can factor these numbers into their prime factors. The prime factorization of 96 is 2 x 2 x 2 x 2 x 2 x 3, and the prime factorization of 64 is 2 x 2 x 2 x 2 x 2 x 2. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 x 2 x 2 x 2 = 32. Therefore, the GCF of Pair B is 32.

This statement is incorrect because the GCF of Pair A is 4, and the GCF of Pair C is 12. They are not the same.

This statement is correct. We found earlier that the GCF of Pair C is indeed 12.

Hence the correct option is (c).

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