What is the Greatest Common Factor of 49707 and 49714?

Greatest common factor (GCF) of 49707 and 49714 is 7.

GCF(49707,49714) = 7

We will now calculate the prime factors of 49707 and 49714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49707 and 49714.

How to find the GCF of 49707 and 49714?

We will first find the prime factorization of 49707 and 49714. After we will calculate the factors of 49707 and 49714 and find the biggest common factor number .

Step-1: Prime Factorization of 49707

Prime factors of 49707 are 3, 7, 263. Prime factorization of 49707 in exponential form is:

49707 = 3³ × 7¹ × 263¹

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 49707

List of positive integer factors of 49707 that divides 49707 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189, 263, 789, 1841, 2367, 5523, 7101, 16569

Step-4: Factors of 49714

List of positive integer factors of 49714 that divides 49707 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 49707 and 49714. The biggest common factor number is the GCF number.
So the greatest common factor 49707 and 49714 is 7.

Also check out the Least Common Multiple of 49707 and 49714