What is the Greatest Common Factor of 40689 and 40704?

Greatest common factor (GCF) of 40689 and 40704 is 3.

GCF(40689,40704) = 3

We will now calculate the prime factors of 40689 and 40704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40689 and 40704.

How to find the GCF of 40689 and 40704?

We will first find the prime factorization of 40689 and 40704. After we will calculate the factors of 40689 and 40704 and find the biggest common factor number .

Step-1: Prime Factorization of 40689

Prime factors of 40689 are 3, 11, 137. Prime factorization of 40689 in exponential form is:

40689 = 3³ × 11¹ × 137¹

Step-2: Prime Factorization of 40704

Prime factors of 40704 are 2, 3, 53. Prime factorization of 40704 in exponential form is:

40704 = 2⁸ × 3¹ × 53¹

Step-3: Factors of 40689

List of positive integer factors of 40689 that divides 40689 without a remainder.

1, 3, 9, 11, 27, 33, 99, 137, 297, 411, 1233, 1507, 3699, 4521, 13563

Step-4: Factors of 40704

List of positive integer factors of 40704 that divides 40689 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 53, 64, 96, 106, 128, 159, 192, 212, 256, 318, 384, 424, 636, 768, 848, 1272, 1696, 2544, 3392, 5088, 6784, 10176, 13568, 20352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 40689 and 40704. The biggest common factor number is the GCF number.
So the greatest common factor 40689 and 40704 is 3.

Also check out the Least Common Multiple of 40689 and 40704