What is the Greatest Common Factor of 1742 and 1755?

Greatest common factor (GCF) of 1742 and 1755 is 13.

GCF(1742,1755) = 13

We will now calculate the prime factors of 1742 and 1755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1742 and 1755.

How to find the GCF of 1742 and 1755?

We will first find the prime factorization of 1742 and 1755. After we will calculate the factors of 1742 and 1755 and find the biggest common factor number .

Step-1: Prime Factorization of 1742

Prime factors of 1742 are 2, 13, 67. Prime factorization of 1742 in exponential form is:

1742 = 2¹ × 13¹ × 67¹

Step-2: Prime Factorization of 1755

Prime factors of 1755 are 3, 5, 13. Prime factorization of 1755 in exponential form is:

1755 = 3³ × 5¹ × 13¹

Step-3: Factors of 1742

List of positive integer factors of 1742 that divides 1742 without a remainder.

1, 2, 13, 26, 67, 134, 871

Step-4: Factors of 1755

List of positive integer factors of 1755 that divides 1742 without a remainder.

1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1742 and 1755. The biggest common factor number is the GCF number.
So the greatest common factor 1742 and 1755 is 13.

Also check out the Least Common Multiple of 1742 and 1755