What is the Greatest Common Factor of 29640 and 29659?

Greatest common factor (GCF) of 29640 and 29659 is 19.

GCF(29640,29659) = 19

We will now calculate the prime factors of 29640 and 29659, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29640 and 29659.

How to find the GCF of 29640 and 29659?

We will first find the prime factorization of 29640 and 29659. After we will calculate the factors of 29640 and 29659 and find the biggest common factor number .

Step-1: Prime Factorization of 29640

Prime factors of 29640 are 2, 3, 5, 13, 19. Prime factorization of 29640 in exponential form is:

29640 = 2³ × 3¹ × 5¹ × 13¹ × 19¹

Step-2: Prime Factorization of 29659

Prime factors of 29659 are 7, 19, 223. Prime factorization of 29659 in exponential form is:

29659 = 7¹ × 19¹ × 223¹

Step-3: Factors of 29640

List of positive integer factors of 29640 that divides 29640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 19, 20, 24, 26, 30, 38, 39, 40, 52, 57, 60, 65, 76, 78, 95, 104, 114, 120, 130, 152, 156, 190, 195, 228, 247, 260, 285, 312, 380, 390, 456, 494, 520, 570, 741, 760, 780, 988, 1140, 1235, 1482, 1560, 1976, 2280, 2470, 2964, 3705, 4940, 5928, 7410, 9880, 14820

Step-4: Factors of 29659

List of positive integer factors of 29659 that divides 29640 without a remainder.

1, 7, 19, 133, 223, 1561, 4237

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29640 and 29659. The biggest common factor number is the GCF number.
So the greatest common factor 29640 and 29659 is 19.

Also check out the Least Common Multiple of 29640 and 29659