Question

If 146 is divisible by 6n then find the maximum value of n

Answer 1

Let us consider the following equation:
146/(6^n) = x
If 146 is divisible by (6^n), the x has to be an integer, and not a decimal or a fraction.
The factor of 146 should be the same as of 6^n’s factors.
Factors of 146: 2,73
Factors of 6^n: 2^n, 3^n
As 73 is a prime number, only 1 and 73 are divisible to 73.
No multiple of 2 and 3 divide 73 perfectly.
Thus we definitely can get a value of n but it won’t be a positive integer.
Now because we want the maximum value of n, the term 6^n has to be maximum.
The maximum number 146 is divisible by is 146 itself.
Hence 146=(6^n)
By Logarithms,
log(146)=n log(6)
n=2.16435285578/0.77815125038
n=2.7814
Maximum value of n= 2.7814

Answer 2

Let us consider the following equation:

146/(6^n) = x

If 146 is divisible by (6^n), the x has to be an integer, and not a decimal or a fraction.

The factor of 146 should be the same as of 6^n’s factors.

Factors of 146: 2,73

Factors of 6^n: 2^n, 3^n

As 73 is a prime number, only 1 and 73 are divisible to 73.

No multiple of 2 and 3 divide 73 perfectly.

Thus we definitely can get a value of n but it won’t be a positive integer.

Now because we want the maximum value of n, the term 6^n has to be maximum.

The maximum number 146 is divisible by is 146 itself.

Hence 146=(6^n)

By Logarithms,

log(146)=n log(6)

n=2.16435285578/0.77815125038

n=2.7814