Question

Compute the prime factorization of: gcd(38603578125, 52093125)

Answer 1

To compute the prime factorization of the gcd(38603578125, 52093125), find the prime factorization of each number, identify the common prime factors, and multiply them together.

Step-by-step explanation:

To compute the prime factorization of the greatest common divisor (gcd) of two numbers, we start by finding the prime factorization of each number individually. Then, we identify the common prime factors and multiply them together.

1. Let's find the prime factorization of 38603578125: We can begin by dividing it by 5, giving us 7720715625. Continuing in this way, we find that the prime factorization of 38603578125 is 58 * 172 * 3372.
2. Now, let's find the prime factorization of 52093125: We can begin by dividing it by 5, giving us 10418625. Continuing in this way, we find that the prime factorization of 52093125 is 53 * 112 * 372.
3. Next, we identify the common prime factors: In this case, the prime factors 5, 17, and 337 are common to both numbers.
4. Finally, we multiply the common prime factors together to get the prime factorization of the gcd(38603578125, 52093125): 5 * 17 * 337 = 28645.