What is the Greatest Common Factor of 35609 and 35616?

Greatest common factor (GCF) of 35609 and 35616 is 7.

GCF(35609,35616) = 7

We will now calculate the prime factors of 35609 and 35616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35609 and 35616.

How to find the GCF of 35609 and 35616?

We will first find the prime factorization of 35609 and 35616. After we will calculate the factors of 35609 and 35616 and find the biggest common factor number .

Step-1: Prime Factorization of 35609

Prime factors of 35609 are 7, 5087. Prime factorization of 35609 in exponential form is:

35609 = 7¹ × 5087¹

Step-2: Prime Factorization of 35616

Prime factors of 35616 are 2, 3, 7, 53. Prime factorization of 35616 in exponential form is:

35616 = 2⁵ × 3¹ × 7¹ × 53¹

Step-3: Factors of 35609

List of positive integer factors of 35609 that divides 35609 without a remainder.

1, 7, 5087

Step-4: Factors of 35616

List of positive integer factors of 35616 that divides 35609 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 53, 56, 84, 96, 106, 112, 159, 168, 212, 224, 318, 336, 371, 424, 636, 672, 742, 848, 1113, 1272, 1484, 1696, 2226, 2544, 2968, 4452, 5088, 5936, 8904, 11872, 17808

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35609 and 35616. The biggest common factor number is the GCF number.
So the greatest common factor 35609 and 35616 is 7.

Also check out the Least Common Multiple of 35609 and 35616