What is the Greatest Common Factor of 59340 and 59360?

Greatest common factor (GCF) of 59340 and 59360 is 20.

GCF(59340,59360) = 20

We will now calculate the prime factors of 59340 and 59360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59340 and 59360.

How to find the GCF of 59340 and 59360?

We will first find the prime factorization of 59340 and 59360. After we will calculate the factors of 59340 and 59360 and find the biggest common factor number .

Step-1: Prime Factorization of 59340

Prime factors of 59340 are 2, 3, 5, 23, 43. Prime factorization of 59340 in exponential form is:

59340 = 2² × 3¹ × 5¹ × 23¹ × 43¹

Step-2: Prime Factorization of 59360

Prime factors of 59360 are 2, 5, 7, 53. Prime factorization of 59360 in exponential form is:

59360 = 2⁵ × 5¹ × 7¹ × 53¹

Step-3: Factors of 59340

List of positive integer factors of 59340 that divides 59340 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 43, 46, 60, 69, 86, 92, 115, 129, 138, 172, 215, 230, 258, 276, 345, 430, 460, 516, 645, 690, 860, 989, 1290, 1380, 1978, 2580, 2967, 3956, 4945, 5934, 9890, 11868, 14835, 19780, 29670

Step-4: Factors of 59360

List of positive integer factors of 59360 that divides 59340 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 53, 56, 70, 80, 106, 112, 140, 160, 212, 224, 265, 280, 371, 424, 530, 560, 742, 848, 1060, 1120, 1484, 1696, 1855, 2120, 2968, 3710, 4240, 5936, 7420, 8480, 11872, 14840, 29680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59340 and 59360. The biggest common factor number is the GCF number.
So the greatest common factor 59340 and 59360 is 20.

Also check out the Least Common Multiple of 59340 and 59360