Practice30Create account

Neha and Arjun made the two different factor trees of 120 shown. Which statement is correct?

Class 10Fundamental Theorem of ArithmeticNumber Systems
  • ANeha's tree is wrong, because a factor tree must start by splitting off 2
  • BBoth trees end in the primes 2, 2, 2, 3, 5: the prime factorisation is unique apart from order
  • CThe trees end in different primes, so 120 has two prime factorisations
  • DNeha gets and Arjun gets

Step-by-Step Solution

Neha: ; Arjun: . Both give . By the Fundamental Theorem of Arithmetic the primes are always the same; only the order of splitting differs.
Answer: B) Both trees end in the primes 2, 2, 2, 3, 5: the prime factorisation is unique apart from order

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 Fundamental Theorem of Arithmetic practice questions

More Class 10 Fundamental Theorem of Arithmetic practice

In the factor tree shown, the circled numbers are primes. Find the value of x.The prime blocks of 6, 6² and 6³ are shown, and below them the blocks of 10, a number…The division ladders of 72, 108 and 180 are shown. What are HCF(72, 108, 180) and…The prime blocks of 84 and 90 are shown; the blocks they share are outlined in orange,…The factor tree of 360 is shown. Using its prime-power form, how many factors (divisors)…