What is the Greatest Common Factor of 31344 and 31360?

Greatest common factor (GCF) of 31344 and 31360 is 16.

GCF(31344,31360) = 16

We will now calculate the prime factors of 31344 and 31360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31344 and 31360.

How to find the GCF of 31344 and 31360?

We will first find the prime factorization of 31344 and 31360. After we will calculate the factors of 31344 and 31360 and find the biggest common factor number .

Step-1: Prime Factorization of 31344

Prime factors of 31344 are 2, 3, 653. Prime factorization of 31344 in exponential form is:

31344 = 2⁴ × 3¹ × 653¹

Step-2: Prime Factorization of 31360

Prime factors of 31360 are 2, 5, 7. Prime factorization of 31360 in exponential form is:

31360 = 2⁷ × 5¹ × 7²

Step-3: Factors of 31344

List of positive integer factors of 31344 that divides 31344 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 653, 1306, 1959, 2612, 3918, 5224, 7836, 10448, 15672

Step-4: Factors of 31360

List of positive integer factors of 31360 that divides 31344 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 64, 70, 80, 98, 112, 128, 140, 160, 196, 224, 245, 280, 320, 392, 448, 490, 560, 640, 784, 896, 980, 1120, 1568, 1960, 2240, 3136, 3920, 4480, 6272, 7840, 15680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31344 and 31360. The biggest common factor number is the GCF number.
So the greatest common factor 31344 and 31360 is 16.

Also check out the Least Common Multiple of 31344 and 31360