Question

Total factors, divisio
82. Find the total number of factors of 1080, divisible by 15.
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Answer 1

Answer:

Step-by-step explanation:

Step 1

Find the prime factorization of the number 1,080.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree

1,080 he prime factorization in exponential form is: 23 x 33 x 51

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

1,080 = 23 x 33 x 51

Down Arrow

d(n) = (a + 1)(b + 1)(c + 1)

Down Arrow

d(1080) = (3 + 1)(3 + 1)(1 + 1)

Down Arrow

d(1080) = (4)(4)(2)

Down Arrow

d(1080) = 32