What is the Greatest Common Factor of 49735 and 49749?

Greatest common factor (GCF) of 49735 and 49749 is 7.

GCF(49735,49749) = 7

We will now calculate the prime factors of 49735 and 49749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49735 and 49749.

How to find the GCF of 49735 and 49749?

We will first find the prime factorization of 49735 and 49749. After we will calculate the factors of 49735 and 49749 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 49749

Prime factors of 49749 are 3, 7, 23, 103. Prime factorization of 49749 in exponential form is:

49749 = 3¹ × 7¹ × 23¹ × 103¹

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 49749

List of positive integer factors of 49749 that divides 49735 without a remainder.

1, 3, 7, 21, 23, 69, 103, 161, 309, 483, 721, 2163, 2369, 7107, 16583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49735 and 49749. The biggest common factor number is the GCF number.
So the greatest common factor 49735 and 49749 is 7.

Also check out the Least Common Multiple of 49735 and 49749