We can find a given number of factors using the following steps.
Step 1: Do the prime factorization of the given number, i.e., express it as the product of primes.
Step 3: Write the prime factorization in the exponent form.
Step 3: Add 1 to each of the exponents.
Step 4: Multiply all the resultant numbers. This product gives the number of factors of the given number.
Example: Find the number of factors of the number 108.
Solution: Let us find the number of factors of 108 using the steps given below.
Step 1: The prime factorization of the number 108 gives us 108 = 2 × 2 × 3 × 3 × 3
Step 2: After writing the prime factorization in the exponent form we get, 108 = 22 × 33
Step 3: After adding 1 to each of the exponents, 2 and 3 we get (2 + 1) = 3, (3 + 1) = 4.
Step 4: Now multiply these numbers: 3 × 4 = 12. Therefore, the number of factors of 108 is 12.
We can verify this number by writing the actual factors of 108 which are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. Here, 108 has 12 factors, hence, we have verified that 108 has 12 factors.
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First, prime factorize the number. Take the exponent values, add one, and then find their product
Example: 54=2^1 x 3^3
(1+1)(3+1)= 2 * 4
Therefore, 54 has 8 factors
Theory: This is kind of finding the number of combinations possible. You add one because you need to include the single values of the prime numbers
in 54, that would mean 1*2 or 1*3.
