How to Find the Number of Factories in a Number

If you know how, finding the number of factors in a number is as simple as counting 1 2 3. But with larger numbers, you can’t just count each factor. This is a good trick to be able to find the number of factors in an integer.

Table of Contents

Steps

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Choose a number. It can be any number, but it’s best to start with simpler numbers.

For example, choose 72. However, it can also be treated as a variable.

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Find the prime factor of the selected number. There are many ways to do that, but usually, creating a factor tree is the simplest. According to number theory, this is an efficient method because every integer (except -1, 0 and 1) has a certain number of prime factors, and when multiplied together, the product is exactly that number. Remember that 0 and 1 are not prime numbers.

72 is broken down into 2 and 36; 2, 6 and 6; and finally: 2, 2, 3, 2, 3, which is equivalent to 2 ³ *3 ² .

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Take every exponent and add one to each number.

In the example 2 ³ and 3 ² , the exponents are 3 and 2 – adding one to each number gives 4 and 3.

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Get the total of the adjusted exponents..

4 x 3 = 12. 72 has 12 factors – 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

For example

7540

Factorize into primes – 2 ² 5(29)(13). Because x ¹ = x, 29, 13, and 5 all have exponents of 1.
Add 1 to the exponent. 3, 2, 2, 2.
Get the adjusted exponent total. 7540 has 24 factors.

15802

Factorize to prime – 2(7901).
Adjust the exponent – 2, 2.
Add. The number 15802 has four factors – 1, 2, 7901, 15802. 7901 is a prime number.

Advice

The reason for adding one to each exponent is because the power of a number is zero. That is, for 2 ³ , it is possible to decompose into four power combinations: 2 ⁰ , 2 ¹ , 2 ² and 2 ³ . You can multiply 2 ⁰ by 72 and still get 72 by x ⁰ = 1 (with 0 ⁰ being the special exception – it’s an unspecified case)
This article tells you how many factors are in a number without showing how to Break a Number into Factories.

Steps

For example

7540

15802

Advice

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