Basic number theory concepts Factor Common factors GCF

Basic number theory concepts Factor, Common factors, GCF Divisors, Common divisors Multiple, Common multiples, LCM Prime vs composite Odd vs even

Factor or divisor Note: These names may be used interchangeably, except in a context like A divided by B, we call B the divisor and not a factor • • A part 2 is a factor of 6 The numbers that you skip counted by to land on the number Skip count by 2’s—land on 4, 6, 8, etc. . so 2 is a factor of 4, 6, 8, etc….

Common factor (divisor) • A factor that 2 or more numbers share • 2 is a common factor of 4 & 6

GCF (GCD) • Look at the common factors of 2 numbers, the largest is the GCF • The GCF of 12 &18 is 6 because their common factors are 1, 2, 3, 6 and 6 is biggest • Take 12 and look at the numbers underneath it (and closest to it) that you can skip count by and land on 12, the biggest one that lands on 12 and 18 is the GCF

Multiple • To expand • The multiples of 12 are 12, 24, 36, etc. . • The numbers you land on when you skip count by a given number

Common multiple • The common numbers landed on when skip counting by two different numbers

LCM • The first number landed on by both numbers you are skip counting by

Prime vs composite • Prime has only one rectangle associated to it —the long one • Composite has more than one rectangle • 1 is neither prime nor composite • Composite means part

Odd vs even • Even—think pairs • Odd—odd man out, a pair is incomplete

Your project • Use the ideas that you generated with your class work • Start working on this in class • You will finish this outside of class and should expect to spend at least an extra 6 hours on it • It should be typed, but diagrams can (and most likely should be for times sake) be hand written in nicely • Neatness does count

Your project • For each concept (i. e. multiple) make sure to include how EACH model that applies (i. e. skip counting, tile sequences, arrays, and/or rods) does explain the concept and include diagrams • For each concept, don’t forget your metaphor and explain how it does not work and does work. See the next slide for an example metaphor and explanation.

Metaphor for “multiplication” Multiplication is letting a rabbit have a new litter of the same size over and over… Explanation: Multiplication is just repeated addition, where I add the same quantity (hence the litter has to be the same size) to itself a prescribed number of times. So 2 x 3 is 3 added to itself twice. The “ 3” would be the litter size and the rabbit would produce 2 litters. This is where my metaphor breaks down, I say over and over when really each product restricts me to how many times I have the rabbit produce a new litter. Now also, the number of rabbits in a litter can vary and the poor rabbit might get tired of having new little ones to take care of so the process will end for the rabbit.