How many different prime factors does 3150 have?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Split the number into its prime factors; each prime is counted once, however many times it appears.
3150 → \(3150\div2=1575\), \(1575\div3=525\), \(525\div3=175\), \(175\div5=35\), \(35\div5=7\), \(7\div7=1\)
\(3150=2\times3^{2}\times5^{2}\times7\)
Different primes: 2, 3, 5, 7
3150 has 4 different prime factors.
Why the other options are incorrect
Option (1) 5 — Incorrect. 3150 has only 4 different primes (2, 3, 5, 7); no other prime divides it.
Option (3) 6 — Incorrect. This counts the prime factors with repetition (6 in all); the different primes are only 2, 3, 5, 7.
Option (4) 3 — Incorrect. This misses one of the primes; 3150 has 4 different primes: 2, 3, 5, 7.