Math Question find n?

n! = 3! × 5! × 7! = 2⁸ × 3⁴ × 5² × 7 = 2 × 3 × 2² × 5 × 2×3 × 7 × 2³ × 9 × 2×5, so n = 10

Otherwise:

11 is not a factor of n!, so n<11.

7! is an apparent factor of n! (as it is stated), so 7≤n<11.

2⁸ is a factor of n! so 2, 4, 6, and 8 are together factors of n!, with a factor of 2 remaining, so 8≤n<11 and potentially n=10.

3⁴ is a factor of n! so 3, 6, and 9 are together factors of n!, so 9≤n<11 and still potentially n=10.

5² is a factor of n! so 5 and 10 are together factors of n!, so n=10.

n! = (3!)(5!)(7!)

n! = 3,628,800

Integer solution:

n = 10

n! = (3!)(5!)(7!)

n! = 7! * 2 * 3 * 2 * 3 * 4 * 5

n! = 7! * 8 * 9 * 10

n! = 10!

n = 10

It's that simple Idk why you would try anything else.

n! = (3!)(5!)(7!)

n! = (3)(2)(5)(4)(3)(2)(7!)

n! = (2)(5)(3)(3)(4)(2)(7!)

n! = [(2)(5)][(3)(3)][(4)(2)](7!)

n! = (10)(9)(8)(7!)

n! = 10!

n = 10

n ! = 362880

n = 9