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Factors

Factors. Greatest Common Factor & Least Common Multiple. Factors are natural numbers you can multiply together to get another number. Example: 3 * 4 = 12, so 3 and 4 are factors of 12. Factor. Every number has at least two factors What are those two factors every number has? Prime –

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Factors

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  1. Factors Greatest Common Factor & Least Common Multiple

  2. Factors are natural numbers you can multiply together to get another number. • Example: 3 * 4 = 12, so 3 and 4 are factors of 12 Factor

  3. Every number has at least two factors • What are those two factors every number has? • Prime – • Composite - Any number that has only 1 and itself as a factor. A number in which it has more factors other than 1 and itself. Factors

  4. abbreviated GCF • definition – the largest natural number that is a factor of all numbers in a group • examples – 18 is the GCF of 36 and 54 1 is the GCF of 7, 13, and 21 Greatest Common Factor

  5. There are two ways to find the GCF and LCM: • Listing Factors/Multiples Method • Prime Factorization Method How To Find GCF & LCM

  6. abbreviation – LCM • definition – the smallest natural number that is a multiple of all the number in the group (i.e. the smallest number that all the numbers go into) • examples – 30 is the LCM of 15 and 10 25 is the LCM of 5 and 25 Least Common Multiple

  7. Find the GCF and LCM of 12 and 18 Listing Factors/Multiples

  8. Write the prime factorization of each number • Choose all primes common to all factorizations, with each prime raised to the least exponent that it has in any factorization • Find the product of all the numbers. This is your GCF Finding the GCF

  9. Find the GCF of 1800 and 21000. Step 1: Find the prime factorization of each number. 1800 = 23 * 32 * 52 21000 = 23 * 3 * 53 * 7 Step 2: Find all primes in common and raise them to the lowest exponent. 1800 = 23 * 32 * 52 21000 = 23 * 3 * 53 * 7 Step 3: Find the product. 23 * 3 * 52 = 600 The GCF of 1800 and 21000 is 600 Example

  10. 12, 18, 60 • 90, 168 Find the GCF.

  11. Write the prime factorization of each number • Choose all primes belonging to any factorization, with each prime raised to the largest exponent that it has in any factorization • Find the product of all the number. This is your LCM Finding the LCM

  12. Find the LCM of 24 and 38. Step 1: Find the prime factorization of each number. 24= 23 * 3 38 = 2 * 19 Step 2: Find all primes raised to the highest power. 24 = 23 * 3 38 = 2 * 19 Step 3: Find the product. 23 * 3 * 19 = 456 The LCM of 24 and 38 is 456 Example

  13. 12, 18, 60 • 90, 168 Find the LCM.

  14. Worksheet #1 - 15 Homework

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