What is the Greatest Common Factor of 1640 and 1649?

Greatest common factor (GCF) of 1640 and 1649 is 1.

GCF(1640,1649) = 1

We will now calculate the prime factors of 1640 and 1649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1640 and 1649.

How to find the GCF of 1640 and 1649?

We will first find the prime factorization of 1640 and 1649. After we will calculate the factors of 1640 and 1649 and find the biggest common factor number .

Step-1: Prime Factorization of 1640

Prime factors of 1640 are 2, 5, 41. Prime factorization of 1640 in exponential form is:

1640 = 2³ × 5¹ × 41¹

Step-2: Prime Factorization of 1649

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

1649 = 17¹ × 97¹

Step-3: Factors of 1640

List of positive integer factors of 1640 that divides 1640 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 41, 82, 164, 205, 328, 410, 820

Step-4: Factors of 1649

List of positive integer factors of 1649 that divides 1640 without a remainder.

1, 17, 97

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1640 and 1649. The biggest common factor number is the GCF number.
So the greatest common factor 1640 and 1649 is 1.

Also check out the Least Common Multiple of 1640 and 1649