What is the Greatest Common Factor of 417 and 434?

Greatest common factor (GCF) of 417 and 434 is 1.

GCF(417,434) = 1

We will now calculate the prime factors of 417 and 434, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 417 and 434.

How to find the GCF of 417 and 434?

We will first find the prime factorization of 417 and 434. After we will calculate the factors of 417 and 434 and find the biggest common factor number .

Step-1: Prime Factorization of 417

Prime factors of 417 are 3, 139. Prime factorization of 417 in exponential form is:

417 = 3¹ × 139¹

Step-2: Prime Factorization of 434

Prime factors of 434 are 2, 7, 31. Prime factorization of 434 in exponential form is:

434 = 2¹ × 7¹ × 31¹

Step-3: Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1, 3, 139

Step-4: Factors of 434

List of positive integer factors of 434 that divides 417 without a remainder.

1, 2, 7, 14, 31, 62, 217

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 417 and 434. The biggest common factor number is the GCF number.
So the greatest common factor 417 and 434 is 1.

Also check out the Least Common Multiple of 417 and 434