What is the Greatest Common Factor of 31635 and 31654?

Greatest common factor (GCF) of 31635 and 31654 is 19.

GCF(31635,31654) = 19

We will now calculate the prime factors of 31635 and 31654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31635 and 31654.

How to find the GCF of 31635 and 31654?

We will first find the prime factorization of 31635 and 31654. After we will calculate the factors of 31635 and 31654 and find the biggest common factor number .

Step-1: Prime Factorization of 31635

Prime factors of 31635 are 3, 5, 19, 37. Prime factorization of 31635 in exponential form is:

31635 = 3² × 5¹ × 19¹ × 37¹

Step-2: Prime Factorization of 31654

Prime factors of 31654 are 2, 7, 17, 19. Prime factorization of 31654 in exponential form is:

31654 = 2¹ × 7² × 17¹ × 19¹

Step-3: Factors of 31635

List of positive integer factors of 31635 that divides 31635 without a remainder.

1, 3, 5, 9, 15, 19, 37, 45, 57, 95, 111, 171, 185, 285, 333, 555, 703, 855, 1665, 2109, 3515, 6327, 10545

Step-4: Factors of 31654

List of positive integer factors of 31654 that divides 31635 without a remainder.

1, 2, 7, 14, 17, 19, 34, 38, 49, 98, 119, 133, 238, 266, 323, 646, 833, 931, 1666, 1862, 2261, 4522, 15827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31635 and 31654. The biggest common factor number is the GCF number.
So the greatest common factor 31635 and 31654 is 19.

Also check out the Least Common Multiple of 31635 and 31654