How many natural numbers less than 200 have exactly three factors.1. 6

1.	How many natural numbers less than 200 have exactly three factors.1. 62. 663. 144. 7
Answer» Correct Answer - Option 1 : 6 Given: Numbers have exactly 3 factors Concept used: If the number can be expressed as xa.yb.zc, where x, y, and z are prime numbers and a, b, and c are whole numbers, Then total number of factors of the number = (a + 1) × (b + 1) × (c + 1) Numbers having only 3 factors can be expressed as x², here x is a prime number. Calculation: As the numbers have only three factors ⇒ Numbers are of the form x², here x is a prime number ⇒ Total number of factors of the number = 2 + 1 = 3, i.e. x, x², and 1 ⇒ 2² = 4, 32 = 9, 52 = 25, 72 = 49, 112 = 121, 132 = 169 ⇒ Natural number which are less than 200 having 3 factors are 4, 9, 25, 49, 121, 169 ∴ There are 6 natural numbers which are lass than 200 and have exactly 3 factors.

How many natural numbers less than 200 have exactly three factors.1. 62. 663. 144. 7

Answer» Correct Answer - Option 1 : 6

Given:

Numbers have exactly 3 factors

Concept used:

If the number can be expressed as xa.yb.zc, where x, y, and z are prime numbers and a, b, and c are whole numbers,

Then total number of factors of the number = (a + 1) × (b + 1) × (c + 1)

Numbers having only 3 factors can be expressed as x², here x is a prime number.

Calculation:

As the numbers have only three factors

⇒ Numbers are of the form x², here x is a prime number

⇒ Total number of factors of the number = 2 + 1 = 3, i.e. x, x², and 1

⇒ 2² = 4, 32 = 9, 52 = 25, 72 = 49, 112 = 121, 132 = 169

⇒ Natural number which are less than 200 having 3 factors are 4, 9, 25, 49, 121, 169

∴ There are 6 natural numbers which are lass than 200 and have exactly 3 factors.

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