What is the Greatest Common Factor of 35735 and 35749?

Greatest common factor (GCF) of 35735 and 35749 is 7.

GCF(35735,35749) = 7

We will now calculate the prime factors of 35735 and 35749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35735 and 35749.

How to find the GCF of 35735 and 35749?

We will first find the prime factorization of 35735 and 35749. After we will calculate the factors of 35735 and 35749 and find the biggest common factor number .

Step-1: Prime Factorization of 35735

Prime factors of 35735 are 5, 7, 1021. Prime factorization of 35735 in exponential form is:

35735 = 5¹ × 7¹ × 1021¹

Step-2: Prime Factorization of 35749

Prime factors of 35749 are 7, 5107. Prime factorization of 35749 in exponential form is:

35749 = 7¹ × 5107¹

Step-3: Factors of 35735

List of positive integer factors of 35735 that divides 35735 without a remainder.

1, 5, 7, 35, 1021, 5105, 7147

Step-4: Factors of 35749

List of positive integer factors of 35749 that divides 35735 without a remainder.

1, 7, 5107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35735 and 35749. The biggest common factor number is the GCF number.
So the greatest common factor 35735 and 35749 is 7.

Also check out the Least Common Multiple of 35735 and 35749