What is the Greatest Common Factor of 53130 and 53144?

Greatest common factor (GCF) of 53130 and 53144 is 14.

GCF(53130,53144) = 14

We will now calculate the prime factors of 53130 and 53144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53130 and 53144.

How to find the GCF of 53130 and 53144?

We will first find the prime factorization of 53130 and 53144. After we will calculate the factors of 53130 and 53144 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 53144

Prime factors of 53144 are 2, 7, 13, 73. Prime factorization of 53144 in exponential form is:

53144 = 2³ × 7¹ × 13¹ × 73¹

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 53144

List of positive integer factors of 53144 that divides 53130 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 73, 91, 104, 146, 182, 292, 364, 511, 584, 728, 949, 1022, 1898, 2044, 3796, 4088, 6643, 7592, 13286, 26572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53130 and 53144. The biggest common factor number is the GCF number.
So the greatest common factor 53130 and 53144 is 14.

Also check out the Least Common Multiple of 53130 and 53144