What is the Greatest Common Factor of 10735 and 10749?

Greatest common factor (GCF) of 10735 and 10749 is 1.

GCF(10735,10749) = 1

We will now calculate the prime factors of 10735 and 10749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10735 and 10749.

How to find the GCF of 10735 and 10749?

We will first find the prime factorization of 10735 and 10749. After we will calculate the factors of 10735 and 10749 and find the biggest common factor number .

Step-1: Prime Factorization of 10735

Prime factors of 10735 are 5, 19, 113. Prime factorization of 10735 in exponential form is:

10735 = 5¹ × 19¹ × 113¹

Step-2: Prime Factorization of 10749

Prime factors of 10749 are 3, 3583. Prime factorization of 10749 in exponential form is:

10749 = 3¹ × 3583¹

Step-3: Factors of 10735

List of positive integer factors of 10735 that divides 10735 without a remainder.

1, 5, 19, 95, 113, 565, 2147

Step-4: Factors of 10749

List of positive integer factors of 10749 that divides 10735 without a remainder.

1, 3, 3583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10735 and 10749. The biggest common factor number is the GCF number.
So the greatest common factor 10735 and 10749 is 1.

Also check out the Least Common Multiple of 10735 and 10749