What is the Greatest Common Factor of 49700 and 49714?

Greatest common factor (GCF) of 49700 and 49714 is 14.

GCF(49700,49714) = 14

We will now calculate the prime factors of 49700 and 49714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49700 and 49714.

How to find the GCF of 49700 and 49714?

We will first find the prime factorization of 49700 and 49714. After we will calculate the factors of 49700 and 49714 and find the biggest common factor number .

Step-1: Prime Factorization of 49700

Prime factors of 49700 are 2, 5, 7, 71. Prime factorization of 49700 in exponential form is:

49700 = 2² × 5² × 7¹ × 71¹

Step-2: Prime Factorization of 49714

Prime factors of 49714 are 2, 7, 53, 67. Prime factorization of 49714 in exponential form is:

49714 = 2¹ × 7¹ × 53¹ × 67¹

Step-3: Factors of 49700

List of positive integer factors of 49700 that divides 49700 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 71, 100, 140, 142, 175, 284, 350, 355, 497, 700, 710, 994, 1420, 1775, 1988, 2485, 3550, 4970, 7100, 9940, 12425, 24850

Step-4: Factors of 49714

List of positive integer factors of 49714 that divides 49700 without a remainder.

1, 2, 7, 14, 53, 67, 106, 134, 371, 469, 742, 938, 3551, 7102, 24857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49700 and 49714. The biggest common factor number is the GCF number.
So the greatest common factor 49700 and 49714 is 14.

Also check out the Least Common Multiple of 49700 and 49714