Question

(a) State Fundamental theorem of Arithmetic.
(b) Using Euclid's division algorithm, find the largest number that divides 1251,
9377 and 15628 leaving remainders 1, 2 and 3, respectively.​

Answer 1

Answer:

(a) The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes (Hardy and Wright 1979, pp. This theorem is also called the unique factorization theorem.

(b) 625 is the largest number that divides 1251, 9377 and 15628 leaving remainder 1, 2 and 3, respectively. So, the correct answer is “625”.