What is the Greatest Common Factor of 29400 and 29419?

Greatest common factor (GCF) of 29400 and 29419 is 1.

GCF(29400,29419) = 1

We will now calculate the prime factors of 29400 and 29419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29400 and 29419.

How to find the GCF of 29400 and 29419?

We will first find the prime factorization of 29400 and 29419. After we will calculate the factors of 29400 and 29419 and find the biggest common factor number .

Step-1: Prime Factorization of 29400

Prime factors of 29400 are 2, 3, 5, 7. Prime factorization of 29400 in exponential form is:

29400 = 2³ × 3¹ × 5² × 7²

Step-2: Prime Factorization of 29419

Prime factors of 29419 are 13, 31, 73. Prime factorization of 29419 in exponential form is:

29419 = 13¹ × 31¹ × 73¹

Step-3: Factors of 29400

List of positive integer factors of 29400 that divides 29400 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 49, 50, 56, 60, 70, 75, 84, 98, 100, 105, 120, 140, 147, 150, 168, 175, 196, 200, 210, 245, 280, 294, 300, 350, 392, 420, 490, 525, 588, 600, 700, 735, 840, 980, 1050, 1176, 1225, 1400, 1470, 1960, 2100, 2450, 2940, 3675, 4200, 4900, 5880, 7350, 9800, 14700

Step-4: Factors of 29419

List of positive integer factors of 29419 that divides 29400 without a remainder.

1, 13, 31, 73, 403, 949, 2263

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29400 and 29419. The biggest common factor number is the GCF number.
So the greatest common factor 29400 and 29419 is 1.

Also check out the Least Common Multiple of 29400 and 29419