What is the Greatest Common Factor of 69730 and 69750?

Greatest common factor (GCF) of 69730 and 69750 is 10.

GCF(69730,69750) = 10

We will now calculate the prime factors of 69730 and 69750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69730 and 69750.

How to find the GCF of 69730 and 69750?

We will first find the prime factorization of 69730 and 69750. After we will calculate the factors of 69730 and 69750 and find the biggest common factor number .

Step-1: Prime Factorization of 69730

Prime factors of 69730 are 2, 5, 19, 367. Prime factorization of 69730 in exponential form is:

69730 = 2¹ × 5¹ × 19¹ × 367¹

Step-2: Prime Factorization of 69750

Prime factors of 69750 are 2, 3, 5, 31. Prime factorization of 69750 in exponential form is:

69750 = 2¹ × 3² × 5³ × 31¹

Step-3: Factors of 69730

List of positive integer factors of 69730 that divides 69730 without a remainder.

1, 2, 5, 10, 19, 38, 95, 190, 367, 734, 1835, 3670, 6973, 13946, 34865

Step-4: Factors of 69750

List of positive integer factors of 69750 that divides 69730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 31, 45, 50, 62, 75, 90, 93, 125, 150, 155, 186, 225, 250, 279, 310, 375, 450, 465, 558, 750, 775, 930, 1125, 1395, 1550, 2250, 2325, 2790, 3875, 4650, 6975, 7750, 11625, 13950, 23250, 34875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69730 and 69750. The biggest common factor number is the GCF number.
So the greatest common factor 69730 and 69750 is 10.

Also check out the Least Common Multiple of 69730 and 69750