1.

The highest common factor of 117 and another number is 13. The second number cannot be which of the following:1. 1692. 1433. 1564. 130

Answer» Correct Answer - Option 3 : 156

Given:

HCF = 13

One number = 117

Concept Used:

Number 1 = HCF× (a) 

Number 2 = HCF× (b)  

Calculation:

Let the ratio of two numbers be a : b 

here 'a' and 'b' are co-prime numbers.

1st number = 117 and HCF = 13

⇒ 117 = 13 × a

⇒ a = 9

Now b will be a co-prime number of 9

Now comparing with the options,

Option 1 = 169 

⇒ 169 =  13 × b

⇒ b = 13

9 and 13 are co-prime numbers.

Hence the second number can be = 169

Now option 2 =143

⇒ 143 = 13 × b

⇒ b = 11

9 and 11 are co-prime numbers.

Hence the second number can be = 143

Now option 4 = 130

⇒ 130 = 13 × b

⇒ b = 10

9 and 10 are co-prime numbers.

Now option 3 = 156

⇒ 156 = 13 × b

⇒ b = 12

9 and 12 are not co-prime numbers.

∴ 156 cannot be a second number.


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