Express 4620 as a product of its prime factors.

Class 10Real NumbersNumber Systems

A $2^{2} \times 3 \times 5 \times 7 \times 11$
B $2 \times 3^{2} \times 5 \times 7 \times 11$
C $2^{2} \times 3 \times 5^{2} \times 7 \times 11$
D $2^{3} \times 3 \times 5 \times 7 \times 11$

Step-by-Step Solution

4620 =

4 \times 1155

, and

1155 = 3 \times 385 = 3 \times 5 \times 77 = 3 \times 5 \times 7 \times 11

. So

4620 = 2^{2} \times 3 \times 5 \times 7 \times 11

(check: 4·3·5·7·11 = 4620). The other options multiply out to 6930, 23100 and 9240 — an easy way to eliminate them.

Answer: A)

2^{2} \times 3 \times 5 \times 7 \times 11

Key idea: Fundamental Theorem of Arithmetic

**Theorem**: Every composite number can be expressed as a product of primes — UNIQUELY, up to the order of factors.

Example:

360 = 2^{3} \times 3^{2} \times 5

. There is no other set of primes whose product is 360.

**Consequences**:
1. **Finding HCF** by primes: HCF = product of LOWEST powers of common primes.
2. **Finding LCM** by primes: LCM = product of HIGHEST powers of all primes appearing.
3. **Identity**: HCF(a,b) × LCM(a,b) =

a \times b

.

Example:

a = 12 = 2^{2} \cdot 3, b = 18 = 2 \cdot 3^{2}

. HCF = 2·3 = 6, LCM =

2^{2} \cdot 3^{2} = 36

. Check:

6 \times 36 = 216 = 12 \times 18

. ✓

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Real Numbers practice questions

More Class 10 Real Numbers practice

Why is 1 deliberately NOT counted as a prime number?In the prime factorisation of 3750, the exponent of 5 is:While drawing a factor tree, a student stopped at 1440 = 2⁵ × 45 and called it the prime…In a factor tree the top number 1001 branches into 7 and x, and then x branches into 11…Which of these numbers CANNOT be written as a product of two DISTINCT prime numbers?