Login

the number 3 power 13 -3 power 10 is divisible by

By Prime factorization ,

313 - 310 = 310(33 - 1) = 310*26 = 2*310*13

So, it is divisible by 2, 13 and 3n, if n ϵ {1, 10}

  • 10
View Full Answer
Hi
  • -3
Ans is 2,3,13
  • -5
Make this question easy for understanding and clear.....
  • 3
3 to the power 13 - 3 to the power 10 is divisible by
  • -2

3¹³  - 3¹⁰

= 3⁽¹⁰⁺³⁾ - 3¹⁰

= 3¹⁰ * 3³  - 3¹⁰
Taking common

= 3¹⁰ ( 3³ - 1)
3³ = 27

= 3¹⁰ ( 27 - 1)

= 3¹⁰ * 26

= 3¹⁰ * 2 *  13

Factors are 2  , 3 , 13

Divisible by 2 , 3 & 13

 

The number 3¹³ - 3¹⁰ is divisible by 2, 3 and 13​

  • 2
What are you looking for?