Do the following numbers share common factors? If so, which is the greatest common factor?:
{240, 96, 144}

Question

Mila Anderson · Accepted Answer

Common factors are #{1,2,3,4,6,8,12,16,24,48}# and hence
Greatest Common Factor is #48#.

Factors of #240# are #{1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240}# Factors of #96# are #{1,2,3,4,6,8,12,16,24,32,48,96}# Factors of #144# are #{1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}# Hence common factors are #{1,2,3,4,6,8,12,16,24,48}# Greatest Common Factor is #48#.

Gabriel Agustin · Answer

undefined To find the greatest common factor (GCF) of the numbers 240, 96, and 144, we need to identify the common factors among these numbers and then determine the greatest one.

The prime factorization of each number is:
- 240 = 2^4 × 3 × 5
- 96 = 2^5 × 3
- 144 = 2^4 × 3^2

The common factors among these numbers are 2 and 3 raised to the smallest power they appear in any of the numbers' factorizations.

Thus, the greatest common factor (GCF) of 240, 96, and 144 is 2^4 × 3, which is equal to 48.

Levi Adams · Answer

undefined Yes, the numbers 240, 96, and 144 share common factors. To find the greatest common factor (GCF), we can use prime factorization.

Prime factorization of each number:
- 240: $2^4 \times 3 \times 5$
- 96: $2^5 \times 3$
- 144: $2^4 \times 3^2$

Common factors among these numbers are formed by the lowest powers of the common prime factors:
- $2^4 \times 3$

Therefore, the greatest common factor (GCF) of 240, 96, and 144 is $2^4 \times 3$, which equals 48.

Do the following numbers share common factors? If so, which is the greatest common factor?: {240, 96, 144}