Sage-Tips

What is the highest power of 7 in 500 factorial?

Answer Submitted without leaving a remainder is 832.

What is the highest power of 3 in 150 factorial?

The highest power of three that would go into our 150 is 4, because 3^ 4 = 81, and 3^5 = 243.

What is the highest power of 7?

Hence the highest power of 7 that can divide 5000! without leaving a remainder is 832.

How do you find the highest power of a number in 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’.

What is the highest power of 7 in 150 17?

You can just find out no. of terms using A.P. Hence, highest power of 7 in 150! is 24.

What is the highest power of 72 in 200?

The Largest power of 72 contained in 200! is 2.

What is the highest power of 6 in 50 factorial?

Step-by-step explanation: 22 is the correct answer.

What is the highest power of 8 in 80 factorial?

I think nine is the highest power of 8 contained in 80!

What is the highest power of 72 in 72 factorial?

Answer & Solution 72 = 8 × 9.

What is the highest power of 5 in 100 factorial?

Step 2

• The highest power of 2 is 100! = = 50 + 25 + 12 + 6 + 3 +1= 97.
• And, the highest power of 5 in 100! = = 20 + 4 = 24.
• Hence, the highest power of 2 in 100! is 97 i.e. 100! contains 97 twos or and the highest power of 5 in 100! is 24 i.e. 100! Contains 24 fives or .

What is the highest power of 7 divides 77?

The highest power of 7 in 77! is 12.

What is the highest power of 24 in 150?

Answer & Solution As the powers of 8 are less, powers of 24 in 150! = 48.

What is the power of 7 in the prime factorization of 150?

There is only one power of 7 (or any other number, for that matter) in the prime factorization of 150! (or any number). The power of a prime number p in the prime factorization of a number n!, n ∈ N, is given by the following formula.

How do you find the highest power of a factorial?

Calculating Highest power of a number in a factorial. If p is prime number, then the highest power of p in a factorial n is given by [ n p] + [ n p 2] + [ n p 3] + … Calculation of the maximum power of a prime number in a factorial simply involves using the formula described above.

What is the highest power of 7 in 150?

Hence, highest power of 7 in 150! is 24. 25 insanely cool gadgets selling out quickly in 2021. We’ve put together a list of incredible gadgets that you didn’t know you needed!

What is the highest power of 7 that can divide 5000?

Hence the highest power of 7 that can divide 5000! without leaving a remainder is 832. 1. Factors, divisors; Prime Factors 2. Test of divisibility by 3, 4, 5 and 7