how to find common factors and common multiples for prime factorization.

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Factors-a number can be evenly divided without a remainder

Examples: Factors of 16 are 2, 4, 8. Factors of 24 are 2, 3, 4, 6, 8, 12.
Multiples-result of multiplying by a whole number.
Examples: Multiples of 2 are 2, 4, 6, 8, 10, etc. See how you are just counting by 2's? Multiples of 6 are 6, 12, 18, 24, 30, etc.

Common are obviously the ones that each number has in common. List both, like I did above, and see which numbers are in both groups. Post specific questions with your answer if you'd like them checked.

To find the common factors and common multiples for prime factorization, you'll first need to understand prime factorization.

Prime factorization is a process of breaking down a number into its prime factors. Prime factors are the prime numbers that multiply together to give the original number.

Here's a step-by-step guide on how to find common factors and common multiples using prime factorization:

1. Start by finding the prime factorization of each number separately. For example, let's say we have two numbers: 36 and 48.

- The prime factorization of 36 is 2^2 * 3^2 (which means 2 to the power of 2 multiplied by 3 to the power of 2).
- The prime factorization of 48 is 2^4 * 3^1 (which means 2 to the power of 4 multiplied by 3 to the power of 1).

2. List out the common prime factors. In this case, the common prime factors are 2 and 3. These are the prime factors that appear in both factorizations.

3. Find the smallest exponent for each prime factor that appears in both factorizations. In this case, 2 appears with an exponent of 2 in the prime factorization of 36 and with an exponent of 4 in the prime factorization of 48. So, we take the smallest exponent, which is 2, as the common factor for 2.

4. Multiply all the common factors together. In this case, since both 2 and 3 are common factors, we multiply 2 * 3 = 6. So, 6 is the common factor of 36 and 48.

5. To find the common multiples, multiply the highest exponent of each prime factor that appears in both factorizations. In this case, 2 appears with an exponent of 2 in the prime factorization of 36 and with an exponent of 4 in the prime factorization of 48. So, we take the highest exponent, which is 4, as the common multiple for 2.

6. Multiply all the common multiples together. In this case, since both 2 and 3 are common factors, we multiply 2^4 * 3^1 = 48. So, 48 is the common multiple of 36 and 48.

By following these steps, you can find the common factors and common multiples using prime factorization.