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"The multiples and factors (or divisors) of a number are the other counting numbers that are related to it by multiplication and division" (Beckman, 2022). For example if you start with a counting number such as 20 you can get other counting numbers by multiplying.
The factors of 30
The factors of 30
If A = B x C then...
How do we find multiples of large numbers?
One way to find out is to divide the counting number by all the counting numbers smaller than it, looking for the ones that divide evenly. For example to find all the factors of 30, divide 30 by 1, by 2, by 3, by 4 and so on keeping track of the numbers that divide evenly.
As seen to the left 30 was divided up until the number 6. After that you don't need to continue going through numbers because any counting number higher than 6 that divides into 30 evenly would have a qoutient less than 5 and already be used.
Teaching factors and multiples in creative ways such as grouping physical objects that are laying around (beads, buttons, M&Ms, coins...) can help aid in understanding the concept. Multiples are in the name, multiplying or making more of the same number where as factors are numbers that fold into each other evenly. Students often get the terms confused or forget that the counting number itself and 1 are a factor pair. I would revisit this topic throughout the year to ensure students have mastered the concept.
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