What is the Greatest Common Factor of 416 and 429?

Greatest common factor (GCF) of 416 and 429 is 13.

GCF(416,429) = 13

We will now calculate the prime factors of 416 and 429, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 416 and 429.

How to find the GCF of 416 and 429?

We will first find the prime factorization of 416 and 429. After we will calculate the factors of 416 and 429 and find the biggest common factor number .

Step-1: Prime Factorization of 416

Prime factors of 416 are 2, 13. Prime factorization of 416 in exponential form is:

416 = 2⁵ × 13¹

Step-2: Prime Factorization of 429

Prime factors of 429 are 3, 11, 13. Prime factorization of 429 in exponential form is:

429 = 3¹ × 11¹ × 13¹

Step-3: Factors of 416

List of positive integer factors of 416 that divides 416 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208

Step-4: Factors of 429

List of positive integer factors of 429 that divides 416 without a remainder.

1, 3, 11, 13, 33, 39, 143

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 416 and 429. The biggest common factor number is the GCF number.
So the greatest common factor 416 and 429 is 13.

Also check out the Least Common Multiple of 416 and 429