N is a number such that 1 x 2 x 3 x 4 x 5 x 6 x 7 = 8 X 9 X 10 X N. What is the value of N?

N = 7

Step-by-step explanation:

1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 = 8 ⋅ 9 ⋅ 10 × N

Multiply 1 and 2 to get 2.

2 × 3 × 4 × 5 × 6 × 7 = 8 × 9 × 10N

Multiply 2 and 3 to get 6.

6 × 4 × 5 × 6 × 7 = 8 × 9 × 10N

Multiply 6 and 4 to get 24.

24 × 5 × 6 × 7 = 8 × 9 × 10N

Multiply 24 and 5 to get 120.

120 × 6 × 7 = 8 × 9 × 10N

Multiply 120 and 6 to get 720.

720 × 7 = 8 × 9 × 10N

Multiply 720 and 7 to get 5040.

5040 = 8 × 9 × 10N

Multiply 8 and 9 to get 72.

5040 = 72 × 10N

Multiply 72 and 10 to get 720.

5040 = 720N

Swap sides so that all variable terms are on the left hand side.

720N = 5040

Divide both sides by 720.

N=

Divide 5040 by 720 to get 7.

N = 7

Hope I was able to help. =D

Have a good night!