Factors

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Presentation transcript:

Factors 􀀹 0506.2.2 Use the prime factorization of two whole numbers to determine the greatest common factor and the least common multiple.

Factors Factor: Any one of the numbers multiplied in a multiplication problem. Factor: A whole number that divides another whole number without a remainder.

Prime Numbers A counting number greater than 1, whose only two factors are the number 1 and itself. Examples: 2: 1x2 3: 1x3 5: 1x5 7: 1x7 11: 1x11

Composite Number A counting number greater than 1 that is divisible by a number other than itself and 1. Every composite number has at least three factors. Every composite number can be expressed as a product of two or more prime numbers. Examples: 4: 1, 2, 4 6: 1, 2, 3, 6

Greatest Common Factor (GCF) The largest whole number that is a factor of two or more given numbers. Example 15: 1, 3, 5, 15 20: 1, 2, 4, 5, 10, 20 What factors do 15 and 20 have in common? 1 and 5 Which one of the factors is greatest or largest? 5, therefore 5 is the Greatest Common Factor

Least Common Multiple (LCM) The smallest whole number that is a multiple of two or more given numbers. Reminder: A multiple is a product of a counting number and another number. Example: The multiples of 3: 3, 6, 9, 12, 15, 18, 21, …

LCM Find the LCM of 4 and 6 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, … 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, … What multiples do 4 and 6 have in common? 12, 24, 36 Which is the least or smallest? 12

Your Turn Find the Greatest Common Factor of 12 and 15. 12: 1, 2, 3, 4, 6, 12 15: 1, 3, 5, 15 The GCF of 12 and 15 is 3 Find the Least Common Multiple of 6 and 8. 6: 6. 12, 18, 24, 30, … 8: 8, 16, 24, 32, 40, … The LCM of 6 and 8 is 24