What is the Greatest Common Factor of 31354 and 31360?

Greatest common factor (GCF) of 31354 and 31360 is 2.

GCF(31354,31360) = 2

We will now calculate the prime factors of 31354 and 31360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31354 and 31360.

How to find the GCF of 31354 and 31360?

We will first find the prime factorization of 31354 and 31360. After we will calculate the factors of 31354 and 31360 and find the biggest common factor number .

Step-1: Prime Factorization of 31354

Prime factors of 31354 are 2, 61, 257. Prime factorization of 31354 in exponential form is:

31354 = 2¹ × 61¹ × 257¹

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 31354

List of positive integer factors of 31354 that divides 31354 without a remainder.

1, 2, 61, 122, 257, 514, 15677

Step-4: Factors of 31360

List of positive integer factors of 31360 that divides 31354 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 31354 and 31360. The biggest common factor number is the GCF number.
So the greatest common factor 31354 and 31360 is 2.

Also check out the Least Common Multiple of 31354 and 31360