To find the factors of a number from its prime factorization, you need to follow these steps:
1. Write down the prime factorization of the number. For example, if the number is 24, its prime factorization is 2^3 * 3^1.
2. List down all the prime factors with their respective exponents. In this case, the prime factors are 2 and 3, with exponents 3 and 1, respectively.
3. For each prime factor, create a list of all possible combinations of its powers. In this case, for the prime factor 2, the powers are 0, 1, 2, and 3. For the prime factor 3, the power is 0 and 1.
4. For each combination of powers, multiply the prime factors raised to those powers. This will give you all the possible factors of the original number.
In the example of 24, the factors are:
2^0 * 3^0 = 1
2^1 * 3^0 = 2
2^2 * 3^0 = 4
2^3 * 3^0 = 8
2^0 * 3^1 = 3
2^1 * 3^1 = 6
2^2 * 3^1 = 12
2^3 * 3^1 = 24
Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
how to find factors of a number from its prime factorisation
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