Highest Power of a Number

Q. The highest power of 12 that completely divides 122! is:

1. 56
2. 57
3. 58
4. 54

Q. The highest power of 7 that completely divides 80! is:

1. 12
2. 14
3. 13
4. 15

Q. $\frac{115}{7^n}$ is an integer. Find the highest possible value of n for this to be true.

1. 16
2. 17
3. 15
4. 18

Q. If 146! is divisible by $5^n$, then find the maximum value of n.

1. 34
2. 36
3. 37
4. 35

Q. The highest power of 45 that will exactly divide 123! is

1. 28
2. 30
3. 31
4. 59

Q. $\frac{53!}{3^n}$ is an integer. Find the highest possible value of n for this to be true.

1. 21
2. 23
3. 24
4. 19

Q. If 146! is divisible by $6^n$, then find the maximum value of n.

1. 76
2. 75
3. 74
4. 70

Q. What is the highest power of 3 available in the expression 58!-38!?

1. 18
2. 19
3. None of these
4. 17

Q. The highest power of 3 that completely divides 40!

1. 17
2. 16
3. 18
4. 15

Q. $\frac{155!}{{20}^n}$ is an integer. Find the highest possible value of n for this to be true.

1. 77
2. 38
3. 75
4. 37