Question

how many prime numbers are contained 36 ×25 ×42​

Answer 1

Answer:

4 prime numbers are contained

Step-by-step explanation:

36=2*3*2*3

25=5*5

42=7*2*3

2,3,5&7

Answer 2

Therefore the given number 36 × 25 × 42 contains '4' non-repetitive primes and '9' repetitive primes.

Given:

The number = 36 × 25 × 42​

To Find:

The number of prime numbers contained by the given number 36 × 25 × 42

Solution:

The given question can be solved very easily as shown below.

Given number = 36 × 25 × 42

Prime factorization of the given numbers,

⇒ 36 = 2 × 3 × 2 × 3

⇒ 25 = 5 × 5

⇒ 42 = 2 × 3 × 7

Then the given number = 36 × 25 × 42 = 2 × 3 × 2 × 3 × 5 × 5 × 2 × 3 × 7

⇒ 36 × 25 × 42 = 2³ × 3³ × 5² × 7

So the number of non-repetitive primes = ( 2, 3, 5, and 7 ) = 4

The number of repetitive primes = 2³ × 3³ × 5² × 7 = Sum of powers of primes = 3 + 3 + 2 + 1 = 9

Therefore the given number 36 × 25 × 42 contains '4' non-repetitive primes and '9' repetitive primes.

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