What is the Greatest Common Factor of 29600 and 29610?

Greatest common factor (GCF) of 29600 and 29610 is 10.

GCF(29600,29610) = 10

We will now calculate the prime factors of 29600 and 29610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29600 and 29610.

How to find the GCF of 29600 and 29610?

We will first find the prime factorization of 29600 and 29610. After we will calculate the factors of 29600 and 29610 and find the biggest common factor number .

Step-1: Prime Factorization of 29600

Prime factors of 29600 are 2, 5, 37. Prime factorization of 29600 in exponential form is:

29600 = 2⁵ × 5² × 37¹

Step-2: Prime Factorization of 29610

Prime factors of 29610 are 2, 3, 5, 7, 47. Prime factorization of 29610 in exponential form is:

29610 = 2¹ × 3² × 5¹ × 7¹ × 47¹

Step-3: Factors of 29600

List of positive integer factors of 29600 that divides 29600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 37, 40, 50, 74, 80, 100, 148, 160, 185, 200, 296, 370, 400, 592, 740, 800, 925, 1184, 1480, 1850, 2960, 3700, 5920, 7400, 14800

Step-4: Factors of 29610

List of positive integer factors of 29610 that divides 29600 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 47, 63, 70, 90, 94, 105, 126, 141, 210, 235, 282, 315, 329, 423, 470, 630, 658, 705, 846, 987, 1410, 1645, 1974, 2115, 2961, 3290, 4230, 4935, 5922, 9870, 14805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29600 and 29610. The biggest common factor number is the GCF number.
So the greatest common factor 29600 and 29610 is 10.

Also check out the Least Common Multiple of 29600 and 29610