SOLUTION: Find the greatest number that divides 1323, 1587, and 1851 leaving exactly 3 as a reminder in each case

Question 1058271: Find the greatest number that divides 1323, 1587, and 1851 leaving exactly 3 as a reminder in each case
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
Taking 3 from each of the three numbers gives:

1323 - 3 = 1320

1587 - 3 = 1584

1851 - 3 = 1848

The prime factorization of the three values (1320, 1584, 1848) is:

1320 = 2^3 * 3 * 5 * 11

1584 = 2^4 * 3^2 * 11

1848 = 2^3 * 3 * 7 * 11

The greatest common factor is found by taking the product of the
highest common factors from the prime factorizations. Those factors
are 2^3, 3, and 11.

GCF = 2^3 * 3 * 11 = 8 * 3 * 11 = 24 * 11 = 264

Solution: The greatest number that divides 1323, 1587, and 1851, each with a remainder of 3 is 264.

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