What is the greatest common factor of 40, 16 ,44
The correct answer and explanation is:
The greatest common factor (GCF) of 40, 16, and 44 is 4.
To determine the GCF, we first find the prime factorization of each number:
- 40: 40 can be divided by 2 multiple times. It can be broken down as:
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1
So, the prime factorization of 40 is 23×52^3 \times 5. - 16: 16 is also a power of 2. It can be broken down as:
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 16 is 242^4. - 44: 44 can be divided by 2 and then by 11:
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
So, the prime factorization of 44 is 22×112^2 \times 11.
Next, to find the GCF, we identify the common prime factors among the three numbers. The only common prime factor among 40, 16, and 44 is 2. Now, we look for the lowest power of 2 that appears in all three factorizations:
- In 40, the power of 2 is 3.
- In 16, the power of 2 is 4.
- In 44, the power of 2 is 2.
The lowest power of 2 is 2, so the GCF is 22=42^2 = 4.
Thus, the greatest common factor of 40, 16, and 44 is 4.