What is the Greatest Common Factor of 49735 and 49742?

Greatest common factor (GCF) of 49735 and 49742 is 7.

GCF(49735,49742) = 7

We will now calculate the prime factors of 49735 and 49742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49735 and 49742.

How to find the GCF of 49735 and 49742?

We will first find the prime factorization of 49735 and 49742. After we will calculate the factors of 49735 and 49742 and find the biggest common factor number .

Step-1: Prime Factorization of 49735

Prime factors of 49735 are 5, 7, 29. Prime factorization of 49735 in exponential form is:

49735 = 5¹ × 7³ × 29¹

Step-2: Prime Factorization of 49742

Prime factors of 49742 are 2, 7, 11, 17, 19. Prime factorization of 49742 in exponential form is:

49742 = 2¹ × 7¹ × 11¹ × 17¹ × 19¹

Step-3: Factors of 49735

List of positive integer factors of 49735 that divides 49735 without a remainder.

1, 5, 7, 29, 35, 49, 145, 203, 245, 343, 1015, 1421, 1715, 7105, 9947

Step-4: Factors of 49742

List of positive integer factors of 49742 that divides 49735 without a remainder.

1, 2, 7, 11, 14, 17, 19, 22, 34, 38, 77, 119, 133, 154, 187, 209, 238, 266, 323, 374, 418, 646, 1309, 1463, 2261, 2618, 2926, 3553, 4522, 7106, 24871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49735 and 49742. The biggest common factor number is the GCF number.
So the greatest common factor 49735 and 49742 is 7.

Also check out the Least Common Multiple of 49735 and 49742