How do you find the greatest power of a factorial?

If we are asked to find the highest power of a number ‘n’ in a factorial, where n is a prime number, we can directly divide the factorial number by ‘n’ (and possible powers of ‘n’) to find the instances of ‘n’, and subsequently the highest power of ‘n’.

How do you find the highest power of a number in another number?

To calculate the highest power of composite number in a factorial, we first express the composite number as a product of primes. Among these prime factors, the highest power of the largest prime factor will be equal to the highest power of that composite number.

What is the greatest power of 30 in 50 factorial?

In the given factorial we have only 12 5s. Hence only twelve 30s are possible. So the greatest power of 30 in 50! is 12.

What is the largest power of 20 obtained in 100 Factorials?

$ 24 $
Hence, the largest power of $ 20 $ contained in $ 100 $ factorial is $ 24 $ . So, the correct answer is “24”.

What is the highest power of 2 Divide 8 100?

the same logic can be applied to find the highest power of any number x that divides n! completely or evenly. therefore, the highest power of 2 that divides 100! is 2^97.

How do you find the next highest power of 2?

next = pow(2, ceil(log(x)/log(2))); This works by finding the number you’d have raise 2 by to get x (take the log of the number, and divide by the log of the desired base, see wikipedia for more). Then round that up with ceil to get the nearest whole number power.

What is the highest power of 54 that divides 31 completely?

So (3^14*2^28) is a multiple of 31!. But we need this in the form of (3^3*2)^n. So the highest power should be (3^3*2)^4=54^4 .

How to find the largest divisor of power 2 in C?

// of 2 that divides n. Approach – 2: This is also an efficient approach, where you can find the largest divisor of power two for a number ‘n’ using a predefined function in C for handling bits. Which is _builtin_ctz (n), this function helps you to find the trailing zeros of the number and then you can see the bits-magic.

How do you find the greatest divisible power of an ugly number?

To find the Greatest Divisible power for an ugly number : Let’s take an example : N=9000 (We want to check this number is ugly or not) , but for that we have to check it by dividing N by the Greatest Divisible Power of prime ( 2,3 or 5) : N=9000 = 2^3 * 3^2 * 5^3. So, GDP of 2 becomes – 2^3 = 8. GDP of 3 becomes – 3^2 = 9.

What is the highest power of 2 that divides 48?

Highest power of 2 that divides 48 is 16. Highest power of 2 that divides 5 is 1. Recommended: Please try your approach on {IDE} first, before moving on to the solution. A simple solution is to try all powers of 2 one by one starting from 1, then 2, then 4 and so on. An efficient solution is based on bit magic.

What is the greatest 5 digit number that is divisible by 100?

999 is the greatest 3-digit number, so 99,900 is the greatest 5-digit number that is divisible by 100. You know you cannot add 4 times 25 to that, as it would be a greater multiple of 100.