For example, if you want to know many divisors, or factors, the number 24 has, write 24{\displaystyle 24} at the top of the page.
For example, 12 and 2 are factors of 24, so draw a split branch coming down from 24{\displaystyle 24}, and write the numbers 12{\displaystyle 12} and 2{\displaystyle 2} below it.
For example, 2 is a prime number, so you would circle the 2{\displaystyle 2} on your factor tree.
For example, 12 can be factored into 6{\displaystyle 6} and 2{\displaystyle 2}. Since 2{\displaystyle 2} is a prime number, you would circle it. Next, 6{\displaystyle 6} can be factored into 3{\displaystyle 3} and 2{\displaystyle 2}. Since 3{\displaystyle 3} and 2{\displaystyle 2} are prime numbers, you would circle them.
For example, the prime factor 2{\displaystyle 2} appears three times in your factor tree, so the exponential expression is 23{\displaystyle 2^{3}}. The prime factor 3{\displaystyle 3} appears 1 time in your factor tree, so the exponential expression is 31{\displaystyle 3^{1}}.
For example 24=23×31{\displaystyle 24=2^{3}\times 3^{1}}.
You might have less than three or more than three exponents. The formula simply states to multiply together whatever number of exponents you are working with.
For example, since 24=23×31{\displaystyle 24=2^{3}\times 3^{1}}, you would plug in the exponents 3{\displaystyle 3} and 1{\displaystyle 1} into the equation. Thus the equation will look like this: d(24)=(3+1)(1+1){\displaystyle d(24)=(3+1)(1+1)}.
For example:d(24)=(3+1)(1+1){\displaystyle d(24)=(3+1)(1+1)}d(24)=(4)(2){\displaystyle d(24)=(4)(2)}
For example:d(24)=(4)(2){\displaystyle d(24)=(4)(2)}d(24)=8{\displaystyle d(24)=8}So, the number of divisors, or factors, in the number 24 is 8.
