What is the Greatest Common Factor of 53120 and 53130?

Greatest common factor (GCF) of 53120 and 53130 is 10.

GCF(53120,53130) = 10

We will now calculate the prime factors of 53120 and 53130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53120 and 53130.

How to find the GCF of 53120 and 53130?

We will first find the prime factorization of 53120 and 53130. After we will calculate the factors of 53120 and 53130 and find the biggest common factor number .

Step-1: Prime Factorization of 53120

Prime factors of 53120 are 2, 5, 83. Prime factorization of 53120 in exponential form is:

53120 = 2⁷ × 5¹ × 83¹

Step-2: 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-3: Factors of 53120

List of positive integer factors of 53120 that divides 53120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 83, 128, 160, 166, 320, 332, 415, 640, 664, 830, 1328, 1660, 2656, 3320, 5312, 6640, 10624, 13280, 26560

Step-4: Factors of 53130

List of positive integer factors of 53130 that divides 53120 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53120 and 53130. The biggest common factor number is the GCF number.
So the greatest common factor 53120 and 53130 is 10.

Also check out the Least Common Multiple of 53120 and 53130