What is the Greatest Common Factor of 1547 and 1564?

Greatest common factor (GCF) of 1547 and 1564 is 17.

GCF(1547,1564) = 17

We will now calculate the prime factors of 1547 and 1564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1547 and 1564.

How to find the GCF of 1547 and 1564?

We will first find the prime factorization of 1547 and 1564. After we will calculate the factors of 1547 and 1564 and find the biggest common factor number .

Step-1: Prime Factorization of 1547

Prime factors of 1547 are 7, 13, 17. Prime factorization of 1547 in exponential form is:

1547 = 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 1564

Prime factors of 1564 are 2, 17, 23. Prime factorization of 1564 in exponential form is:

1564 = 2² × 17¹ × 23¹

Step-3: Factors of 1547

List of positive integer factors of 1547 that divides 1547 without a remainder.

1, 7, 13, 17, 91, 119, 221

Step-4: Factors of 1564

List of positive integer factors of 1564 that divides 1547 without a remainder.

1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1547 and 1564. The biggest common factor number is the GCF number.
So the greatest common factor 1547 and 1564 is 17.

Also check out the Least Common Multiple of 1547 and 1564