What is the Greatest Common Factor of 1649 and 1666?

Greatest common factor (GCF) of 1649 and 1666 is 17.

GCF(1649,1666) = 17

We will now calculate the prime factors of 1649 and 1666, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1649 and 1666.

How to find the GCF of 1649 and 1666?

We will first find the prime factorization of 1649 and 1666. After we will calculate the factors of 1649 and 1666 and find the biggest common factor number .

Step-1: Prime Factorization of 1649

Prime factors of 1649 are 17, 97. Prime factorization of 1649 in exponential form is:

1649 = 17¹ × 97¹

Step-2: Prime Factorization of 1666

Prime factors of 1666 are 2, 7, 17. Prime factorization of 1666 in exponential form is:

1666 = 2¹ × 7² × 17¹

Step-3: Factors of 1649

List of positive integer factors of 1649 that divides 1649 without a remainder.

1, 17, 97

Step-4: Factors of 1666

List of positive integer factors of 1666 that divides 1649 without a remainder.

1, 2, 7, 14, 17, 34, 49, 98, 119, 238, 833

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1649 and 1666. The biggest common factor number is the GCF number.
So the greatest common factor 1649 and 1666 is 17.

Also check out the Least Common Multiple of 1649 and 1666