How many prime factors in all — Aptitude Question
How many prime factors in all: What is the total number of prime factors in the expression 6¹⁰ × 7¹⁷ × 11²⁷? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the total number of prime factors in the expression 6¹⁰ × 7¹⁷ × 11²⁷?
Options
- 54
- 64
- 71
- 81
Show the answer and the worked solution
Correct answer: B. 64
Worked solution
- 6¹⁰ = (2 × 3)¹⁰ = 2¹⁰ × 3¹⁰.
- The expression is 2¹⁰ × 3¹⁰ × 7¹⁷ × 11²⁷.
- Total prime factors counted with multiplicity = 10 + 10 + 17 + 27 = 64.
Answer: 64.
The idea
'Number of prime factors' in these papers means counted with repetition, so it is just the sum of the exponents once every base is prime. The trap is leaving a composite base such as 6 unfactored.
Shortcut. Every power of 6 holds two primes, so count 6's exponent twice: 2 × 10 + 17 + 27 = 64.
Common trap. 54 — adding the exponents 10 + 17 + 27 as they stand, leaving the composite base 6 unsplit.