What is the Greatest Common Factor of 1730 and 1742?

Greatest common factor (GCF) of 1730 and 1742 is 2.

GCF(1730,1742) = 2

We will now calculate the prime factors of 1730 and 1742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1730 and 1742.

How to find the GCF of 1730 and 1742?

We will first find the prime factorization of 1730 and 1742. After we will calculate the factors of 1730 and 1742 and find the biggest common factor number .

Step-1: Prime Factorization of 1730

Prime factors of 1730 are 2, 5, 173. Prime factorization of 1730 in exponential form is:

1730 = 2¹ × 5¹ × 173¹

Step-2: 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-3: Factors of 1730

List of positive integer factors of 1730 that divides 1730 without a remainder.

1, 2, 5, 10, 173, 346, 865

Step-4: Factors of 1742

List of positive integer factors of 1742 that divides 1730 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1730 and 1742. The biggest common factor number is the GCF number.
So the greatest common factor 1730 and 1742 is 2.

Also check out the Least Common Multiple of 1730 and 1742