What is the largest prime factor of 2008?

What is the largest prime factor of 2008?

• A. 199
• B. 223
• C. 251
• D. 257

Answer: (C)

This question tests how to break a number down into prime factors and pick the largest one. Start by pulling out the smallest prime factor. Because 2008 is even, divide by 2 repeatedly: 2008 = 2 × 1004, and 1004 = 2 × 502, and 502 = 2 × 251. What remains after removing all factors of 2 is 251. Now, 251 has no divisors among the primes up to its square root, so it is prime. Therefore the prime factorization is 2^3 × 251, and the largest prime factor is 251. The other choices aren’t factors of 2008, so they can’t be the prime factors.

This question tests how to break a number down into prime factors and pick the largest one. Start by pulling out the smallest prime factor. Because 2008 is even, divide by 2 repeatedly: 2008 = 2 × 1004, and 1004 = 2 × 502, and 502 = 2 × 251. What remains after removing all factors of 2 is 251. Now, 251 has no divisors among the primes up to its square root, so it is prime. Therefore the prime factorization is 2^3 × 251, and the largest prime factor is 251. The other choices aren’t factors of 2008, so they can’t be the prime factors.