The number 3^11-3^8 os divisible by which prime numbers?
a. 2 and 3 only
b. 2,3 and 11 only
c. 3^11 only
d. 2,3 and 13 only.
Please give me the steps without calculator. Thanks in anticipation
Answers
Answered by
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Given,
A given exponential number = 3^11-3^8
To find,
The number by which the given exponential number will be divisible.
Solution,
We can simply solve this mathematical problem using the following process:
On simplifying the given exponential number, we get;
= 3^11-3^8
= 3^8 (3^3-1)
= 3^8 (27-1)
= 3^8 × 26
= 3^8 × (2×13)
= 2 × (3)^8 × 13
=> 2, 3, and 13 are the only prime number factors of the given exponential number
Hence, the given number 3^11-3^8 is divisible by the prime numbers 2,3, and 13, only. (Option-D)
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