What is the Greatest Common Factor of 32312 and 32320?

Greatest common factor (GCF) of 32312 and 32320 is 8.

GCF(32312,32320) = 8

We will now calculate the prime factors of 32312 and 32320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32312 and 32320.

How to find the GCF of 32312 and 32320?

We will first find the prime factorization of 32312 and 32320. After we will calculate the factors of 32312 and 32320 and find the biggest common factor number .

Step-1: Prime Factorization of 32312

Prime factors of 32312 are 2, 7, 577. Prime factorization of 32312 in exponential form is:

32312 = 2³ × 7¹ × 577¹

Step-2: Prime Factorization of 32320

Prime factors of 32320 are 2, 5, 101. Prime factorization of 32320 in exponential form is:

32320 = 2⁶ × 5¹ × 101¹

Step-3: Factors of 32312

List of positive integer factors of 32312 that divides 32312 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 577, 1154, 2308, 4039, 4616, 8078, 16156

Step-4: Factors of 32320

List of positive integer factors of 32320 that divides 32312 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 101, 160, 202, 320, 404, 505, 808, 1010, 1616, 2020, 3232, 4040, 6464, 8080, 16160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32312 and 32320. The biggest common factor number is the GCF number.
So the greatest common factor 32312 and 32320 is 8.

Also check out the Least Common Multiple of 32312 and 32320