What is the Greatest Common Factor of 57400 and 57414?

Greatest common factor (GCF) of 57400 and 57414 is 14.

GCF(57400,57414) = 14

We will now calculate the prime factors of 57400 and 57414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57400 and 57414.

How to find the GCF of 57400 and 57414?

We will first find the prime factorization of 57400 and 57414. After we will calculate the factors of 57400 and 57414 and find the biggest common factor number .

Step-1: Prime Factorization of 57400

Prime factors of 57400 are 2, 5, 7, 41. Prime factorization of 57400 in exponential form is:

57400 = 2³ × 5² × 7¹ × 41¹

Step-2: Prime Factorization of 57414

Prime factors of 57414 are 2, 3, 7, 1367. Prime factorization of 57414 in exponential form is:

57414 = 2¹ × 3¹ × 7¹ × 1367¹

Step-3: Factors of 57400

List of positive integer factors of 57400 that divides 57400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 41, 50, 56, 70, 82, 100, 140, 164, 175, 200, 205, 280, 287, 328, 350, 410, 574, 700, 820, 1025, 1148, 1400, 1435, 1640, 2050, 2296, 2870, 4100, 5740, 7175, 8200, 11480, 14350, 28700

Step-4: Factors of 57414

List of positive integer factors of 57414 that divides 57400 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1367, 2734, 4101, 8202, 9569, 19138, 28707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57400 and 57414. The biggest common factor number is the GCF number.
So the greatest common factor 57400 and 57414 is 14.

Also check out the Least Common Multiple of 57400 and 57414