Skill Rack
Daily MCQ Answer
Date : 27/03/2019
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In how many ways can 1200 be expressed as a product of two co primes?
Answer : 4
Solution:
Prime factors of 1200 = 2*2*2*2*3*5*5
= 2⁴ × 3¹ × 5²
The number of factors of ways writing a number N as a product of two co-primes = 2ⁿ⁻¹ , where N = the number of prime factors of a number.
Number of prime factors of 1200 are 2, 3 and 5
So, total number of prime factors of 1200 = 3
Therefore, total number of ways of writing 1200 as a product of 2 co-primes
= 2ⁿ⁻¹
= 2³⁻¹
= 2²
= 4
So, 1200 can be written in 4 ways as a product of two co-primes.
= 2⁴ × 3¹ × 5²
The number of factors of ways writing a number N as a product of two co-primes = 2ⁿ⁻¹ , where N = the number of prime factors of a number.
Number of prime factors of 1200 are 2, 3 and 5
So, total number of prime factors of 1200 = 3
Therefore, total number of ways of writing 1200 as a product of 2 co-primes
= 2ⁿ⁻¹
= 2³⁻¹
= 2²
= 4
So, 1200 can be written in 4 ways as a product of two co-primes.
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