Transcript Slide 1
Greatest Common Factor Definition: The Greatest Common Factor is the largest number that will divide into two other numbers or the number that contains all the factors common to both numbers. Example: the Greatest Common Factor of 2940 and 3150 is found by finding all the prime numbers they have in common and multiplying them. 2940: 2 x 2 x 3 x 5x7x7 3150:2x3x3x5x5x7 You can see that the numbers in red are what they have in common therefore the Greatest Common Factor is 2x3x5x7 =210 Least Common Multiple • Definition: The Least Common Multiple is the smallest number that two numbers will divide into. In other words all of the factors of the two numbers have to be used. • An example of the Least Common Multiple of 2940 and 3150 are as follows. • 2940: 2 x 2 x 3 x 5x7x7 • 3150:2x3x3x5x5x7 • Therefore the LCM is found by multiplying • 2x2x3x3x5xrx7x7 = 44100 • Caution do not overuse a factor. Don’t count both top and bottom just the maximum times it appears in either the top or bottom. Factor • To factor a number means to break it up into numbers that can be multiplied together to get the original number. • Example 14 = 7x2 so 7 and 2 are factors of 14. Prime Number • A prime number is a natural number greater than 1 that has no positive divisors other than one or itself. • Examples include 7 and 13. Composite Numbers • Composite Numbers are numbers that are Natural Numbers greater than one and not prime. • Examples include 8, and 9. Natural Numbers • Natural numbers: There is some debate as to whether natural numbers include zero or not, but basically they are the positive numbers and do not include fractions. Practice Find the LCM and GCF for each set of numbers 1) 250 332 2)630 358 3) 276 912 4) 77 11