How many factors does 5^3 x 7^4 have?
I get 20. Did you?
that is right but how do you get 20? is there a quick way of doing it
To determine the number of factors that a given number has, we need to consider its prime factorization.
In this case, we have the number 5^3 x 7^4.
To find the prime factorization of a number, we break it down into its prime factors. For example, 12 can be written as 2 x 2 x 3, where 2 and 3 are both prime numbers.
For 5^3 x 7^4, we know that 5 and 7 are both prime numbers. Thus, we can say that the prime factorization of the given number is 5 x 5 x 5 x 7 x 7 x 7 x 7.
To find the number of factors, we can use a formula that involves the exponents of the prime factors.
The formula is given by (a + 1)(b + 1)(c + 1)..., where a, b, c are the exponents of the respective prime factors.
In this case, we have 3 as the exponent for 5 and 4 as the exponent for 7. Applying the formula, we get (3+1)(4+1) = 4 x 5 = 20.
Therefore, the number 5^3 x 7^4 has 20 factors.