What is the Greatest Common Factor of 31641 and 31648?

Greatest common factor (GCF) of 31641 and 31648 is 1.

GCF(31641,31648) = 1

We will now calculate the prime factors of 31641 and 31648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31641 and 31648.

How to find the GCF of 31641 and 31648?

We will first find the prime factorization of 31641 and 31648. After we will calculate the factors of 31641 and 31648 and find the biggest common factor number .

Step-1: Prime Factorization of 31641

Prime factors of 31641 are 3, 53, 199. Prime factorization of 31641 in exponential form is:

31641 = 3¹ × 53¹ × 199¹

Step-2: Prime Factorization of 31648

Prime factors of 31648 are 2, 23, 43. Prime factorization of 31648 in exponential form is:

31648 = 2⁵ × 23¹ × 43¹

Step-3: Factors of 31641

List of positive integer factors of 31641 that divides 31641 without a remainder.

1, 3, 53, 159, 199, 597, 10547

Step-4: Factors of 31648

List of positive integer factors of 31648 that divides 31641 without a remainder.

1, 2, 4, 8, 16, 23, 32, 43, 46, 86, 92, 172, 184, 344, 368, 688, 736, 989, 1376, 1978, 3956, 7912, 15824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31641 and 31648. The biggest common factor number is the GCF number.
So the greatest common factor 31641 and 31648 is 1.

Also check out the Least Common Multiple of 31641 and 31648