What is the Greatest Common Factor of 42700 and 42714?

Greatest common factor (GCF) of 42700 and 42714 is 14.

GCF(42700,42714) = 14

We will now calculate the prime factors of 42700 and 42714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42700 and 42714.

How to find the GCF of 42700 and 42714?

We will first find the prime factorization of 42700 and 42714. After we will calculate the factors of 42700 and 42714 and find the biggest common factor number .

Step-1: Prime Factorization of 42700

Prime factors of 42700 are 2, 5, 7, 61. Prime factorization of 42700 in exponential form is:

42700 = 2² × 5² × 7¹ × 61¹

Step-2: Prime Factorization of 42714

Prime factors of 42714 are 2, 3, 7, 113. Prime factorization of 42714 in exponential form is:

42714 = 2¹ × 3³ × 7¹ × 113¹

Step-3: Factors of 42700

List of positive integer factors of 42700 that divides 42700 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 61, 70, 100, 122, 140, 175, 244, 305, 350, 427, 610, 700, 854, 1220, 1525, 1708, 2135, 3050, 4270, 6100, 8540, 10675, 21350

Step-4: Factors of 42714

List of positive integer factors of 42714 that divides 42700 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 113, 126, 189, 226, 339, 378, 678, 791, 1017, 1582, 2034, 2373, 3051, 4746, 6102, 7119, 14238, 21357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42700 and 42714. The biggest common factor number is the GCF number.
So the greatest common factor 42700 and 42714 is 14.

Also check out the Least Common Multiple of 42700 and 42714