What is the Greatest Common Factor of 1802 and 1819?

Greatest common factor (GCF) of 1802 and 1819 is 17.

GCF(1802,1819) = 17

We will now calculate the prime factors of 1802 and 1819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1802 and 1819.

How to find the GCF of 1802 and 1819?

We will first find the prime factorization of 1802 and 1819. After we will calculate the factors of 1802 and 1819 and find the biggest common factor number .

Step-1: Prime Factorization of 1802

Prime factors of 1802 are 2, 17, 53. Prime factorization of 1802 in exponential form is:

1802 = 2¹ × 17¹ × 53¹

Step-2: Prime Factorization of 1819

Prime factors of 1819 are 17, 107. Prime factorization of 1819 in exponential form is:

1819 = 17¹ × 107¹

Step-3: Factors of 1802

List of positive integer factors of 1802 that divides 1802 without a remainder.

1, 2, 17, 34, 53, 106, 901

Step-4: Factors of 1819

List of positive integer factors of 1819 that divides 1802 without a remainder.

1, 17, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1802 and 1819. The biggest common factor number is the GCF number.
So the greatest common factor 1802 and 1819 is 17.

Also check out the Least Common Multiple of 1802 and 1819