Question

Find the number of non-prime factors of 2^10 x 7^3 x 5^9​

Answer 1

Answer:

1436.

Step-by-step explanation:

Given

N=2

5

×3

7

×9

2

×11

4

×13

3

It can also be written as

N=2

5

×3

11

××11

4

×13

3

To calculate total number of factors adding 1 to each exponent and multiplying, we get

Total number of factors=6×12×5×4=1440

Number of prime factors=4

So,

Number of non-prime factors=1440−4=1436

Therefore total number of non prime factors are 1436.

Answer 2

Answer: 437

Step-by-step explanation:

as we see, given exponents are: 10, 9, 3(if arranged in ascending order), now the question states to find the non-prime factors, a shortcut method for this query is:

1. add +1 to every exponent, we get: (10+1), (9+1), (3+1),
2. now multiply them: (11) * (10) * (4) = 440
3. as we see there are 3 number of factors right (2, 5, 7), so we'll reduce 440 by 3
4. 440 - 3 = 437.
5. this shortcut method works on every question.