What is the Greatest Common Factor of 20735 and 20748?

Greatest common factor (GCF) of 20735 and 20748 is 13.

GCF(20735,20748) = 13

We will now calculate the prime factors of 20735 and 20748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20735 and 20748.

How to find the GCF of 20735 and 20748?

We will first find the prime factorization of 20735 and 20748. After we will calculate the factors of 20735 and 20748 and find the biggest common factor number .

Step-1: Prime Factorization of 20735

Prime factors of 20735 are 5, 11, 13, 29. Prime factorization of 20735 in exponential form is:

20735 = 5¹ × 11¹ × 13¹ × 29¹

Step-2: Prime Factorization of 20748

Prime factors of 20748 are 2, 3, 7, 13, 19. Prime factorization of 20748 in exponential form is:

20748 = 2² × 3¹ × 7¹ × 13¹ × 19¹

Step-3: Factors of 20735

List of positive integer factors of 20735 that divides 20735 without a remainder.

1, 5, 11, 13, 29, 55, 65, 143, 145, 319, 377, 715, 1595, 1885, 4147

Step-4: Factors of 20748

List of positive integer factors of 20748 that divides 20735 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 19, 21, 26, 28, 38, 39, 42, 52, 57, 76, 78, 84, 91, 114, 133, 156, 182, 228, 247, 266, 273, 364, 399, 494, 532, 546, 741, 798, 988, 1092, 1482, 1596, 1729, 2964, 3458, 5187, 6916, 10374

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20735 and 20748. The biggest common factor number is the GCF number.
So the greatest common factor 20735 and 20748 is 13.

Also check out the Least Common Multiple of 20735 and 20748