What is the Greatest Common Factor of 29631 and 29648?

Greatest common factor (GCF) of 29631 and 29648 is 17.

GCF(29631,29648) = 17

We will now calculate the prime factors of 29631 and 29648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29631 and 29648.

How to find the GCF of 29631 and 29648?

We will first find the prime factorization of 29631 and 29648. After we will calculate the factors of 29631 and 29648 and find the biggest common factor number .

Step-1: Prime Factorization of 29631

Prime factors of 29631 are 3, 7, 17, 83. Prime factorization of 29631 in exponential form is:

29631 = 3¹ × 7¹ × 17¹ × 83¹

Step-2: Prime Factorization of 29648

Prime factors of 29648 are 2, 17, 109. Prime factorization of 29648 in exponential form is:

29648 = 2⁴ × 17¹ × 109¹

Step-3: Factors of 29631

List of positive integer factors of 29631 that divides 29631 without a remainder.

1, 3, 7, 17, 21, 51, 83, 119, 249, 357, 581, 1411, 1743, 4233, 9877

Step-4: Factors of 29648

List of positive integer factors of 29648 that divides 29631 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 109, 136, 218, 272, 436, 872, 1744, 1853, 3706, 7412, 14824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29631 and 29648. The biggest common factor number is the GCF number.
So the greatest common factor 29631 and 29648 is 17.

Also check out the Least Common Multiple of 29631 and 29648