What is the Greatest Common Factor of 29785 and 29800?

Greatest common factor (GCF) of 29785 and 29800 is 5.

GCF(29785,29800) = 5

We will now calculate the prime factors of 29785 and 29800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29785 and 29800.

How to find the GCF of 29785 and 29800?

We will first find the prime factorization of 29785 and 29800. After we will calculate the factors of 29785 and 29800 and find the biggest common factor number .

Step-1: Prime Factorization of 29785

Prime factors of 29785 are 5, 7, 23, 37. Prime factorization of 29785 in exponential form is:

29785 = 5¹ × 7¹ × 23¹ × 37¹

Step-2: Prime Factorization of 29800

Prime factors of 29800 are 2, 5, 149. Prime factorization of 29800 in exponential form is:

29800 = 2³ × 5² × 149¹

Step-3: Factors of 29785

List of positive integer factors of 29785 that divides 29785 without a remainder.

1, 5, 7, 23, 35, 37, 115, 161, 185, 259, 805, 851, 1295, 4255, 5957

Step-4: Factors of 29800

List of positive integer factors of 29800 that divides 29785 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 149, 200, 298, 596, 745, 1192, 1490, 2980, 3725, 5960, 7450, 14900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29785 and 29800. The biggest common factor number is the GCF number.
So the greatest common factor 29785 and 29800 is 5.

Also check out the Least Common Multiple of 29785 and 29800