What is the Greatest Common Factor of 17754 and 17770?

Greatest common factor (GCF) of 17754 and 17770 is 2.

GCF(17754,17770) = 2

We will now calculate the prime factors of 17754 and 17770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17754 and 17770.

How to find the GCF of 17754 and 17770?

We will first find the prime factorization of 17754 and 17770. After we will calculate the factors of 17754 and 17770 and find the biggest common factor number .

Step-1: Prime Factorization of 17754

Prime factors of 17754 are 2, 3, 11, 269. Prime factorization of 17754 in exponential form is:

17754 = 2¹ × 3¹ × 11¹ × 269¹

Step-2: Prime Factorization of 17770

Prime factors of 17770 are 2, 5, 1777. Prime factorization of 17770 in exponential form is:

17770 = 2¹ × 5¹ × 1777¹

Step-3: Factors of 17754

List of positive integer factors of 17754 that divides 17754 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 269, 538, 807, 1614, 2959, 5918, 8877

Step-4: Factors of 17770

List of positive integer factors of 17770 that divides 17754 without a remainder.

1, 2, 5, 10, 1777, 3554, 8885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17754 and 17770. The biggest common factor number is the GCF number.
So the greatest common factor 17754 and 17770 is 2.

Also check out the Least Common Multiple of 17754 and 17770