What is the Greatest Common Factor of 17408 and 17420?

Greatest common factor (GCF) of 17408 and 17420 is 4.

GCF(17408,17420) = 4

We will now calculate the prime factors of 17408 and 17420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17408 and 17420.

How to find the GCF of 17408 and 17420?

We will first find the prime factorization of 17408 and 17420. After we will calculate the factors of 17408 and 17420 and find the biggest common factor number .

Step-1: Prime Factorization of 17408

Prime factors of 17408 are 2, 17. Prime factorization of 17408 in exponential form is:

17408 = 2¹⁰ × 17¹

Step-2: Prime Factorization of 17420

Prime factors of 17420 are 2, 5, 13, 67. Prime factorization of 17420 in exponential form is:

17420 = 2² × 5¹ × 13¹ × 67¹

Step-3: Factors of 17408

List of positive integer factors of 17408 that divides 17408 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2176, 4352, 8704

Step-4: Factors of 17420

List of positive integer factors of 17420 that divides 17408 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 67, 130, 134, 260, 268, 335, 670, 871, 1340, 1742, 3484, 4355, 8710

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17408 and 17420. The biggest common factor number is the GCF number.
So the greatest common factor 17408 and 17420 is 4.

Also check out the Least Common Multiple of 17408 and 17420