What is the Greatest Common Factor of 53130 and 53140?

Greatest common factor (GCF) of 53130 and 53140 is 10.

GCF(53130,53140) = 10

We will now calculate the prime factors of 53130 and 53140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53130 and 53140.

How to find the GCF of 53130 and 53140?

We will first find the prime factorization of 53130 and 53140. After we will calculate the factors of 53130 and 53140 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 53140

Prime factors of 53140 are 2, 5, 2657. Prime factorization of 53140 in exponential form is:

53140 = 2² × 5¹ × 2657¹

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 53140

List of positive integer factors of 53140 that divides 53130 without a remainder.

1, 2, 4, 5, 10, 20, 2657, 5314, 10628, 13285, 26570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53130 and 53140. The biggest common factor number is the GCF number.
So the greatest common factor 53130 and 53140 is 10.

Also check out the Least Common Multiple of 53130 and 53140