What is the Greatest Common Factor of 53130 and 53136?

Greatest common factor (GCF) of 53130 and 53136 is 6.

GCF(53130,53136) = 6

We will now calculate the prime factors of 53130 and 53136, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53130 and 53136.

How to find the GCF of 53130 and 53136?

We will first find the prime factorization of 53130 and 53136. After we will calculate the factors of 53130 and 53136 and find the biggest common factor number .

Step-1: Prime Factorization of 53130

Prime factors of 53130 are 2, 3, 5, 7, 11, 23. Prime factorization of 53130 in exponential form is:

53130 = 2¹ × 3¹ × 5¹ × 7¹ × 11¹ × 23¹

Step-2: Prime Factorization of 53136

Prime factors of 53136 are 2, 3, 41. Prime factorization of 53136 in exponential form is:

53136 = 2⁴ × 3⁴ × 41¹

Step-3: Factors of 53130

List of positive integer factors of 53130 that divides 53130 without a remainder.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 23, 30, 33, 35, 42, 46, 55, 66, 69, 70, 77, 105, 110, 115, 138, 154, 161, 165, 210, 230, 231, 253, 322, 330, 345, 385, 462, 483, 506, 690, 759, 770, 805, 966, 1155, 1265, 1518, 1610, 1771, 2310, 2415, 2530, 3542, 3795, 4830, 5313, 7590, 8855, 10626, 17710, 26565

Step-4: Factors of 53136

List of positive integer factors of 53136 that divides 53130 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 41, 48, 54, 72, 81, 82, 108, 123, 144, 162, 164, 216, 246, 324, 328, 369, 432, 492, 648, 656, 738, 984, 1107, 1296, 1476, 1968, 2214, 2952, 3321, 4428, 5904, 6642, 8856, 13284, 17712, 26568

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53130 and 53136. The biggest common factor number is the GCF number.
So the greatest common factor 53130 and 53136 is 6.

Also check out the Least Common Multiple of 53130 and 53136