What is the Greatest Common Factor of 31072 and 31080?

Greatest common factor (GCF) of 31072 and 31080 is 8.

GCF(31072,31080) = 8

We will now calculate the prime factors of 31072 and 31080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31072 and 31080.

How to find the GCF of 31072 and 31080?

We will first find the prime factorization of 31072 and 31080. After we will calculate the factors of 31072 and 31080 and find the biggest common factor number .

Step-1: Prime Factorization of 31072

Prime factors of 31072 are 2, 971. Prime factorization of 31072 in exponential form is:

31072 = 2⁵ × 971¹

Step-2: Prime Factorization of 31080

Prime factors of 31080 are 2, 3, 5, 7, 37. Prime factorization of 31080 in exponential form is:

31080 = 2³ × 3¹ × 5¹ × 7¹ × 37¹

Step-3: Factors of 31072

List of positive integer factors of 31072 that divides 31072 without a remainder.

1, 2, 4, 8, 16, 32, 971, 1942, 3884, 7768, 15536

Step-4: Factors of 31080

List of positive integer factors of 31080 that divides 31072 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 37, 40, 42, 56, 60, 70, 74, 84, 105, 111, 120, 140, 148, 168, 185, 210, 222, 259, 280, 296, 370, 420, 444, 518, 555, 740, 777, 840, 888, 1036, 1110, 1295, 1480, 1554, 2072, 2220, 2590, 3108, 3885, 4440, 5180, 6216, 7770, 10360, 15540

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31072 and 31080. The biggest common factor number is the GCF number.
So the greatest common factor 31072 and 31080 is 8.

Also check out the Least Common Multiple of 31072 and 31080