What is the Greatest Common Factor of 51506 and 51520?

Greatest common factor (GCF) of 51506 and 51520 is 14.

GCF(51506,51520) = 14

We will now calculate the prime factors of 51506 and 51520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51506 and 51520.

How to find the GCF of 51506 and 51520?

We will first find the prime factorization of 51506 and 51520. After we will calculate the factors of 51506 and 51520 and find the biggest common factor number .

Step-1: Prime Factorization of 51506

Prime factors of 51506 are 2, 7, 13, 283. Prime factorization of 51506 in exponential form is:

51506 = 2¹ × 7¹ × 13¹ × 283¹

Step-2: Prime Factorization of 51520

Prime factors of 51520 are 2, 5, 7, 23. Prime factorization of 51520 in exponential form is:

51520 = 2⁶ × 5¹ × 7¹ × 23¹

Step-3: Factors of 51506

List of positive integer factors of 51506 that divides 51506 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 283, 566, 1981, 3679, 3962, 7358, 25753

Step-4: Factors of 51520

List of positive integer factors of 51520 that divides 51506 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 23, 28, 32, 35, 40, 46, 56, 64, 70, 80, 92, 112, 115, 140, 160, 161, 184, 224, 230, 280, 320, 322, 368, 448, 460, 560, 644, 736, 805, 920, 1120, 1288, 1472, 1610, 1840, 2240, 2576, 3220, 3680, 5152, 6440, 7360, 10304, 12880, 25760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51506 and 51520. The biggest common factor number is the GCF number.
So the greatest common factor 51506 and 51520 is 14.

Also check out the Least Common Multiple of 51506 and 51520