What is the Greatest Common Factor of 35649 and 35664?

Greatest common factor (GCF) of 35649 and 35664 is 3.

GCF(35649,35664) = 3

We will now calculate the prime factors of 35649 and 35664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35649 and 35664.

How to find the GCF of 35649 and 35664?

We will first find the prime factorization of 35649 and 35664. After we will calculate the factors of 35649 and 35664 and find the biggest common factor number .

Step-1: Prime Factorization of 35649

Prime factors of 35649 are 3, 17, 233. Prime factorization of 35649 in exponential form is:

35649 = 3² × 17¹ × 233¹

Step-2: Prime Factorization of 35664

Prime factors of 35664 are 2, 3, 743. Prime factorization of 35664 in exponential form is:

35664 = 2⁴ × 3¹ × 743¹

Step-3: Factors of 35649

List of positive integer factors of 35649 that divides 35649 without a remainder.

1, 3, 9, 17, 51, 153, 233, 699, 2097, 3961, 11883

Step-4: Factors of 35664

List of positive integer factors of 35664 that divides 35649 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 743, 1486, 2229, 2972, 4458, 5944, 8916, 11888, 17832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35649 and 35664. The biggest common factor number is the GCF number.
So the greatest common factor 35649 and 35664 is 3.

Also check out the Least Common Multiple of 35649 and 35664