What is the Greatest Common Factor of 42400 and 42414?

Greatest common factor (GCF) of 42400 and 42414 is 2.

GCF(42400,42414) = 2

We will now calculate the prime factors of 42400 and 42414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42400 and 42414.

How to find the GCF of 42400 and 42414?

We will first find the prime factorization of 42400 and 42414. After we will calculate the factors of 42400 and 42414 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 42414

Prime factors of 42414 are 2, 3, 7069. Prime factorization of 42414 in exponential form is:

42414 = 2¹ × 3¹ × 7069¹

Step-3: Factors of 42400

List of positive integer factors of 42400 that divides 42400 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

Step-4: Factors of 42414

List of positive integer factors of 42414 that divides 42400 without a remainder.

1, 2, 3, 6, 7069, 14138, 21207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42400 and 42414. The biggest common factor number is the GCF number.
So the greatest common factor 42400 and 42414 is 2.

Also check out the Least Common Multiple of 42400 and 42414