Find the GCF of the numbers 52 and 405. Show your method.
52 = 2x2x13
405 = 3x3x3x3x5
clearly, there is no common factor
The possibilities are A) 65 B) 26 C) 1 D) 6.
So would it be one?
To find the Greatest Common Factor (GCF) of two numbers, such as 52 and 405, we can use a method called prime factorization. Here's how to do it:
Step 1: Prime factorize each number.
To prime factorize a number, we break it down into its prime factors: the numbers that can divide it evenly without leaving any remainder.
Prime factorization of 52:
52 ÷ 2 = 26
26 ÷ 2 = 13
So, prime factorization of 52 is 2 * 2 * 13, which can be written as 2² * 13.
Prime factorization of 405:
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
So, prime factorization of 405 is 3 * 3 * 3 * 5, which can be written as 3³ * 5.
Step 2: Identify the common prime factors.
Look for the prime factors that the two numbers have in common.
Common prime factors of 52 and 405: 3 (none others are common).
Step 3: Multiply the common prime factors.
Multiply the common prime factors together to find the GCF.
GCF of 52 and 405: 3.
Therefore, the GCF of 52 and 405 is 3.