how to find factors of a number from its prime factorisation
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.
To find the factors of a number from its prime factorization, you can follow these steps:
Step 1: Write down the prime factorization of the given number. For example, let's say the number is 36, and its prime factorization is 2^2 * 3^2.
Step 2: Write down all possible combinations of the powers of the prime factors.
For 2: 2^0, 2^1, 2^2
For 3: 3^0, 3^1, 3^2
Step 3: Multiply all combinations together to get the factors.
2^0 * 3^0 = 1
2^1 * 3^0 = 2
2^2 * 3^0 = 4
2^0 * 3^1 = 3
2^1 * 3^1 = 6
2^2 * 3^1 = 12
2^0 * 3^2 = 9
2^1 * 3^2 = 18
2^2 * 3^2 = 36
Therefore, the factors of 36 from its prime factorization are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
To find the factors of a number given its prime factorization, you need to understand the concept of factors first. Factors are the whole numbers that evenly divide a given number without leaving any remainder.
Here's a step-by-step guide to finding the factors of a number using its prime factorization:
1. Write down the prime factorization of the given number. For example, if the number is 36, the prime factorization would be 2^2 * 3^2 (2 raised to the power of 2 times 3 raised to the power of 2).
2. Identify the individual prime factors and their exponents. In the example, the prime factors are 2 and 3, and their respective exponents are 2 and 2.
3. Create a list of all possible combinations using the prime factors and their exponents. For each prime factor, you can have the exponent range from zero to its given exponent. In the example, you would have these combinations: (2^0 * 3^0), (2^1 * 3^0), (2^2 * 3^0), (2^0 * 3^1), (2^1 * 3^1), (2^2 * 3^1), (2^0 * 3^2), (2^1 * 3^2), (2^2 * 3^2).
4. Simplify each combination to get the actual factors. Multiply the prime factors raised to their respective exponents in each combination. For example, in the combination (2^1 * 3^2), the factor would be 2 * 3 * 3 = 18.
5. Write down all the calculated factors. In the example above, the factors would be 1, 2, 3, 4, 6, 9, 12, 18, 36.
By following these steps, you can find all the factors of a number using its prime factorization.