What is the Greatest Common Factor of 31504 and 31520?

Greatest common factor (GCF) of 31504 and 31520 is 16.

GCF(31504,31520) = 16

We will now calculate the prime factors of 31504 and 31520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31504 and 31520.

How to find the GCF of 31504 and 31520?

We will first find the prime factorization of 31504 and 31520. After we will calculate the factors of 31504 and 31520 and find the biggest common factor number .

Step-1: Prime Factorization of 31504

Prime factors of 31504 are 2, 11, 179. Prime factorization of 31504 in exponential form is:

31504 = 2⁴ × 11¹ × 179¹

Step-2: Prime Factorization of 31520

Prime factors of 31520 are 2, 5, 197. Prime factorization of 31520 in exponential form is:

31520 = 2⁵ × 5¹ × 197¹

Step-3: Factors of 31504

List of positive integer factors of 31504 that divides 31504 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 179, 358, 716, 1432, 1969, 2864, 3938, 7876, 15752

Step-4: Factors of 31520

List of positive integer factors of 31520 that divides 31504 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 197, 394, 788, 985, 1576, 1970, 3152, 3940, 6304, 7880, 15760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31504 and 31520. The biggest common factor number is the GCF number.
So the greatest common factor 31504 and 31520 is 16.

Also check out the Least Common Multiple of 31504 and 31520