what is the GCF 16 and 40
1, 16, 2, 8, 4
1, 40, 2, 20, 4, 10, 5, 8
thanx
To find the Greatest Common Factor (GCF) of two numbers, you can use a method called prime factorization. Here's how you can use this method to find the GCF of 16 and 40:
Step 1: Prime factorization of 16
To find the prime factors of 16, start dividing it by the smallest prime number, which is 2.
16 ÷ 2 = 8
Continue dividing the quotient by 2 until you can no longer divide evenly.
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 16 is 2 × 2 × 2 × 2, which can be written as 2^4.
Step 2: Prime factorization of 40
To find the prime factors of 40, divide it by 2 again.
40 ÷ 2 = 20
Divide the quotient by 2 until you can no longer divide evenly.
20 ÷ 2 = 10
Divide the new quotient by 2 again.
10 ÷ 2 = 5
So, the prime factorization of 40 is 2 × 2 × 2 × 5, which can be written as 2^3 × 5.
Step 3: Finding the GCF
To find the GCF, compare the common prime factors raised to their lowest exponents. In this case, the only common prime factor is 2, and it appears 3 times in the prime factorization of 40 but only 2 times in the prime factorization of 16.
Therefore, the GCF of 16 and 40 is 2^2, which equals 4.
So, the GCF of 16 and 40 is 4.