Track / Stage 3 / 176 of 260 #176 of 1964

Problem 176

AMC 10/12, early questions

Number theory Difficulty 3.6 Find the answer South African Mathematics Olympiad · South Africa

If $4350$ is written as a product of its prime factors, then the largest prime factor is

Pick one

Official solution

Clearly $4350$ is divisible by $5$ , since the last two digits are $50$ . It is also divisible by $3$ , since the sum of the digits is divisible by $3$ . Dividing by $150$ gives a quotient of $29$ , which is prime, so the prime factorization is $4350 = 2 \times 3 \times 5^2 \times 29$ , and the largest prime factor is $29$ .

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