If n! = 720, then find the value of n.
please give a brief answer
Answers
Answer:
Let’s look at the prime factors of 720 to figure this out.
We want to know what factorial equals 720. That is, if you multiply the natural numbers together in ascending order, what is the last number we multiply before our product exactly equals 720? Obviously, not every number can be reached using this method, but that’s okay, if 720 is not the factorial of any number, we will see from the prime factors.
720
= 360 * 2
= 180 * 2 * 2
= 90 * 2 * 2 * 2
= 30 * 3 * 2 * 2 * 2
= 10 * 3 * 3 * 2 * 2 * 2
= 5 * 2 * 3 * 3 * 2 * 2 * 2
Our prime factors are a 5, two 3s, and four 2s. Let’s rearrange these prime factors to form an ascending list of natural numbers. If we can’t, x! ≠ 720 for any x.
1 * 2 * 2 * 2 * 2 * 3 * 3 * 5
= 1 * 2 * 3 * 2 * 2 * 5 * 3 * 2
= (1) * (2) * (3) * (2 * 2) * (5) * (3 * 2)
= 1 * 2 * 3 * 4 * 5 * 6
= 6!
6! = 720, so x! = 720 for x=6.
Answer:
Hope it helps you☺️☺️✌️✌️
