What is the Greatest Common Factor of 35730 and 35742?

Greatest common factor (GCF) of 35730 and 35742 is 6.

GCF(35730,35742) = 6

We will now calculate the prime factors of 35730 and 35742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35730 and 35742.

How to find the GCF of 35730 and 35742?

We will first find the prime factorization of 35730 and 35742. After we will calculate the factors of 35730 and 35742 and find the biggest common factor number .

Step-1: Prime Factorization of 35730

Prime factors of 35730 are 2, 3, 5, 397. Prime factorization of 35730 in exponential form is:

35730 = 2¹ × 3² × 5¹ × 397¹

Step-2: Prime Factorization of 35742

Prime factors of 35742 are 2, 3, 7, 23, 37. Prime factorization of 35742 in exponential form is:

35742 = 2¹ × 3¹ × 7¹ × 23¹ × 37¹

Step-3: Factors of 35730

List of positive integer factors of 35730 that divides 35730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 397, 794, 1191, 1985, 2382, 3573, 3970, 5955, 7146, 11910, 17865

Step-4: Factors of 35742

List of positive integer factors of 35742 that divides 35730 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 37, 42, 46, 69, 74, 111, 138, 161, 222, 259, 322, 483, 518, 777, 851, 966, 1554, 1702, 2553, 5106, 5957, 11914, 17871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35730 and 35742. The biggest common factor number is the GCF number.
So the greatest common factor 35730 and 35742 is 6.

Also check out the Least Common Multiple of 35730 and 35742