How many different prime factors does 4620 have?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
Split the number into its prime factors; each prime is counted once, however many times it appears.
4620 → \(4620\div2=2310\), \(2310\div2=1155\), \(1155\div3=385\), \(385\div5=77\), \(77\div7=11\), \(11\div11=1\)
\(4620=2^{2}\times3\times5\times7\times11\)
Different primes: 2, 3, 5, 7, 11
4620 has 5 different prime factors.
Why the other options are incorrect
Option (1) 6 — Incorrect. This counts the prime factors with repetition (6 in all); the different primes are only 2, 3, 5, 7, 11.
Option (3) 7 — Incorrect. 4620 has only 5 different primes (2, 3, 5, 7, 11); no other prime divides it.
Option (4) 4 — Incorrect. This misses one of the primes; 4620 has 5 different primes: 2, 3, 5, 7, 11.