What is the Greatest Common Factor of 20748 and 20757?

Greatest common factor (GCF) of 20748 and 20757 is 3.

GCF(20748,20757) = 3

We will now calculate the prime factors of 20748 and 20757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20748 and 20757.

How to find the GCF of 20748 and 20757?

We will first find the prime factorization of 20748 and 20757. After we will calculate the factors of 20748 and 20757 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 20757

Prime factors of 20757 are 3, 11, 17, 37. Prime factorization of 20757 in exponential form is:

20757 = 3¹ × 11¹ × 17¹ × 37¹

Step-3: Factors of 20748

List of positive integer factors of 20748 that divides 20748 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

Step-4: Factors of 20757

List of positive integer factors of 20757 that divides 20748 without a remainder.

1, 3, 11, 17, 33, 37, 51, 111, 187, 407, 561, 629, 1221, 1887, 6919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20748 and 20757. The biggest common factor number is the GCF number.
So the greatest common factor 20748 and 20757 is 3.

Also check out the Least Common Multiple of 20748 and 20757