What is the Greatest Common Factor of 42780 and 42800?

Greatest common factor (GCF) of 42780 and 42800 is 20.

GCF(42780,42800) = 20

We will now calculate the prime factors of 42780 and 42800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42780 and 42800.

How to find the GCF of 42780 and 42800?

We will first find the prime factorization of 42780 and 42800. After we will calculate the factors of 42780 and 42800 and find the biggest common factor number .

Step-1: Prime Factorization of 42780

Prime factors of 42780 are 2, 3, 5, 23, 31. Prime factorization of 42780 in exponential form is:

42780 = 2² × 3¹ × 5¹ × 23¹ × 31¹

Step-2: Prime Factorization of 42800

Prime factors of 42800 are 2, 5, 107. Prime factorization of 42800 in exponential form is:

42800 = 2⁴ × 5² × 107¹

Step-3: Factors of 42780

List of positive integer factors of 42780 that divides 42780 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 31, 46, 60, 62, 69, 92, 93, 115, 124, 138, 155, 186, 230, 276, 310, 345, 372, 460, 465, 620, 690, 713, 930, 1380, 1426, 1860, 2139, 2852, 3565, 4278, 7130, 8556, 10695, 14260, 21390

Step-4: Factors of 42800

List of positive integer factors of 42800 that divides 42780 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 107, 200, 214, 400, 428, 535, 856, 1070, 1712, 2140, 2675, 4280, 5350, 8560, 10700, 21400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42780 and 42800. The biggest common factor number is the GCF number.
So the greatest common factor 42780 and 42800 is 20.

Also check out the Least Common Multiple of 42780 and 42800