Q: What is the total or count of factors of the number 147,041,466?

 A: 96

How do I find the total factors of the number 147,041,466?

Step 1

Find the prime factorization of the number 147,041,466.

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

Factor Tree
147,041,466
Factor Arrows
273,520,733
Factor Arrows
324,506,911
Factor Arrows
112,227,901
Factor Arrows
13171,377
Factor Arrows
1710,081
Factor Arrows
17593

The prime factorization in exponential form is: 21 x 31 x 111 x 131 x 172 x 5931

Step 2

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

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 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.

147,041,466 = 21 x 31 x 111 x 131 x 172 x 5931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(147041466) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(147041466) = (2)(2)(2)(2)(3)(2)
Down Arrow
d(147041466) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 147,041,466 and how to find them.

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