What is the Greatest Common Factor of 42380 and 42400?

Greatest common factor (GCF) of 42380 and 42400 is 20.

GCF(42380,42400) = 20

We will now calculate the prime factors of 42380 and 42400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42380 and 42400.

How to find the GCF of 42380 and 42400?

We will first find the prime factorization of 42380 and 42400. After we will calculate the factors of 42380 and 42400 and find the biggest common factor number .

Step-1: Prime Factorization of 42380

Prime factors of 42380 are 2, 5, 13, 163. Prime factorization of 42380 in exponential form is:

42380 = 2² × 5¹ × 13¹ × 163¹

Step-2: Prime Factorization of 42400

Prime factors of 42400 are 2, 5, 53. Prime factorization of 42400 in exponential form is:

42400 = 2⁵ × 5² × 53¹

Step-3: Factors of 42380

List of positive integer factors of 42380 that divides 42380 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 163, 260, 326, 652, 815, 1630, 2119, 3260, 4238, 8476, 10595, 21190

Step-4: Factors of 42400

List of positive integer factors of 42400 that divides 42380 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42380 and 42400. The biggest common factor number is the GCF number.
So the greatest common factor 42380 and 42400 is 20.

Also check out the Least Common Multiple of 42380 and 42400