What is the Greatest Common Factor of 32972 and 32984?

Greatest common factor (GCF) of 32972 and 32984 is 4.

GCF(32972,32984) = 4

We will now calculate the prime factors of 32972 and 32984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32972 and 32984.

How to find the GCF of 32972 and 32984?

We will first find the prime factorization of 32972 and 32984. After we will calculate the factors of 32972 and 32984 and find the biggest common factor number .

Step-1: Prime Factorization of 32972

Prime factors of 32972 are 2, 8243. Prime factorization of 32972 in exponential form is:

32972 = 2² × 8243¹

Step-2: Prime Factorization of 32984

Prime factors of 32984 are 2, 7, 19, 31. Prime factorization of 32984 in exponential form is:

32984 = 2³ × 7¹ × 19¹ × 31¹

Step-3: Factors of 32972

List of positive integer factors of 32972 that divides 32972 without a remainder.

1, 2, 4, 8243, 16486

Step-4: Factors of 32984

List of positive integer factors of 32984 that divides 32972 without a remainder.

1, 2, 4, 7, 8, 14, 19, 28, 31, 38, 56, 62, 76, 124, 133, 152, 217, 248, 266, 434, 532, 589, 868, 1064, 1178, 1736, 2356, 4123, 4712, 8246, 16492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32972 and 32984. The biggest common factor number is the GCF number.
So the greatest common factor 32972 and 32984 is 4.

Also check out the Least Common Multiple of 32972 and 32984