Question

49 to the power 15-1 is exactly divisible by

Answer 1

(49) ^15 -1 is exactly divisible by what number?

Still have a question? Ask your own!

What is your question?

6 ANSWERS



Vipin Chaurasia, former Senior Executive at KPMG India (2015-2017)

Answered Mar 26

49^15–1

Well, we can do it intuitively.

For a number which ends with 9 (Special Property of 9)

If power is even, last digit of the number is 1. (9*9=81)

If power is odd, last digit of the number is 9. (9*9*9=729)

Now we know that 49 ends with 9 and 15 is an odd number

Hence, we can conclude that the last digit of 49^15 is 9. (AN ODD NUMBER)

Now deducting 1 from an odd number makes it an even number.

All even numbers can be divided by 2

Your answer is 2

Thanks

Answer 2

49¹⁵  - 1  is exactly divisible by 48 , 24 , 16 , 12 , 8 , 6 , 4 , 3 , 2

Step-by-step explanation:

49¹⁵  - 1

= (7²)¹⁵ - 1

= 7³⁰ - 1

= (8 - 1)³⁰ - 1

= 8³⁰  + ³⁰C₁ * 8²⁹(-1)¹ +..........................................+³⁰C₂₉*8(-1)²⁹ + (-1)³⁰ - 1

= 8³⁰  - 30 * 8²⁹ +..........................................- 30*8 + 1 - 1

= 8³⁰  - 30 * 8²⁹ +..........................................- 30*8

8 is common factor in all

Hence 49¹⁵  - 1  is exactly divisible by 8

Similalrly 7³⁰ - 1 = (6 + 1)³⁰ - 1  will have 6 as common factor

Hence 7³⁰ - 1   is exactly divisible by 6

LCM of 8 & 6  = 24

49¹⁵  - 1

= (48 + 1)¹⁵  - 1

will have all factors of 48 hence exactly divisible by 48

Learn more:

if a 10 digit number 2094x843y2 divisible by 88 then the value of (5x ...

https://brainly.in/question/11094736

If n3 is multiple of 2, then n is divisible by 2. Prove by any method ...

https://brainly.in/question/12244932