What is the Greatest Common Factor of 53130 and 53138?

Greatest common factor (GCF) of 53130 and 53138 is 2.

GCF(53130,53138) = 2

We will now calculate the prime factors of 53130 and 53138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53130 and 53138.

How to find the GCF of 53130 and 53138?

We will first find the prime factorization of 53130 and 53138. After we will calculate the factors of 53130 and 53138 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 53138

Prime factors of 53138 are 2, 163. Prime factorization of 53138 in exponential form is:

53138 = 2¹ × 163²

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 53138

List of positive integer factors of 53138 that divides 53130 without a remainder.

1, 2, 163, 326, 26569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53130 and 53138. The biggest common factor number is the GCF number.
So the greatest common factor 53130 and 53138 is 2.

Also check out the Least Common Multiple of 53130 and 53138