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Donna Boucher
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Being able to find factors and common factors is an important skill that shows up in a number of areas of mathematics. Students use factors to recognize prime and composite numbers, simplify fractions, find equivalent fractions, and work with common denominators. Understanding factors also helps students see the multiplicative relationships within numbers.
But finding all the factors of a number can be tricky. Students who aren’t fluent with their multiplication facts may struggle to identify factor pairs, but even students who know their facts well can run into trouble. They tend to think of the basic facts they know and may not recognize, for example, that 2 and 18 are factors of 36. And without an organized process, students often skip around from fact to fact and end up leaving some factors out. A simple, structured approach can help students systematically find factor pairs—and know when they’ve found them all.
Start by organizing the work in a T-chart. Write the number you’re finding factors for at the top of the chart.
Then work systematically through each single-digit number, beginning with 1, to determine whether it is a factor. For 36, the conversation might sound something like this:
Is 1 a factor? Yes. 1 and what? 1 and 36.
Is 2 a factor? Yes. How do you know? Because 36 is even. 2 and what? 2 and 18.
Is 3 a factor? Yes. 3 and what? 3 and 12.
Is 4 a factor? Yes. 4 and what? 4 and 9.
Is 5 a factor? No. How do you know? Because 36 doesn’t have a 0 or 5 in the ones place.
Is 6 a factor? Yes. 6 and what? 6 and 6.
Is 7 a factor? No. How do you know? 7×5=357 \times 5 = 35, so 36 isn’t a multiple of 7.
Is 8 a factor? No. How do you know? 8×4=328 \times 4 = 32 and 8×5=408 \times 5 = 40, so 36 falls between two multiples of 8.
Is 9 a factor? Yes—but 9 is already on the list.
And they’re done! By checking each single-digit number in order, students have a consistent process that helps ensure they don’t accidentally leave out factors. When they encounter a factor that’s already on the T-chart, like 9 in this example, they recognize that the factor pair has already been recorded and don’t need to write it again.
Notice that this process requires more than simply recalling multiplication facts. Students can use what they know about even and odd numbers, divisibility rules, and known multiples to determine whether a number is a factor. If they know a number is a factor but don’t immediately know its partner, they can divide to find the missing factor.
Once students have a reliable process for finding all the factors of a number, finding common factors is a natural next step. Create a T-chart for each number and find all the factor pairs using the same process. Then compare the two lists and circle the factors that appear in both. Those are the common factors of the two numbers.
Finding factors becomes much easier when students have a systematic process instead of trying to pull multiplication facts from memory in random order. Working through the numbers in order helps students find all the factor pairs, while also reinforcing multiplication relationships, divisibility, and the connection between multiplication and division.
I’ve put together a free set of number cards you can use for practice. Students can choose one card and use the T-chart strategy to find all the factors of the number. To practice finding common factors, they simply choose two cards, find the factors of each number, and identify the factors the two numbers have in common. Because the numbers can be mixed and matched, the cards provide lots of practice without lots of prep.
The post Finding Factors and Common Factors appeared first on Math Coach's Corner.
But finding all the factors of a number can be tricky. Students who aren’t fluent with their multiplication facts may struggle to identify factor pairs, but even students who know their facts well can run into trouble. They tend to think of the basic facts they know and may not recognize, for example, that 2 and 18 are factors of 36. And without an organized process, students often skip around from fact to fact and end up leaving some factors out. A simple, structured approach can help students systematically find factor pairs—and know when they’ve found them all.
A Structured Process for Finding Factors
Start by organizing the work in a T-chart. Write the number you’re finding factors for at the top of the chart.
Then work systematically through each single-digit number, beginning with 1, to determine whether it is a factor. For 36, the conversation might sound something like this:
Is 1 a factor? Yes. 1 and what? 1 and 36.
Is 2 a factor? Yes. How do you know? Because 36 is even. 2 and what? 2 and 18.
Is 3 a factor? Yes. 3 and what? 3 and 12.
Is 4 a factor? Yes. 4 and what? 4 and 9.
Is 5 a factor? No. How do you know? Because 36 doesn’t have a 0 or 5 in the ones place.
Is 6 a factor? Yes. 6 and what? 6 and 6.
Is 7 a factor? No. How do you know? 7×5=357 \times 5 = 35, so 36 isn’t a multiple of 7.
Is 8 a factor? No. How do you know? 8×4=328 \times 4 = 32 and 8×5=408 \times 5 = 40, so 36 falls between two multiples of 8.
Is 9 a factor? Yes—but 9 is already on the list.
And they’re done! By checking each single-digit number in order, students have a consistent process that helps ensure they don’t accidentally leave out factors. When they encounter a factor that’s already on the T-chart, like 9 in this example, they recognize that the factor pair has already been recorded and don’t need to write it again.
Notice that this process requires more than simply recalling multiplication facts. Students can use what they know about even and odd numbers, divisibility rules, and known multiples to determine whether a number is a factor. If they know a number is a factor but don’t immediately know its partner, they can divide to find the missing factor.
Finding Common Factors
Once students have a reliable process for finding all the factors of a number, finding common factors is a natural next step. Create a T-chart for each number and find all the factor pairs using the same process. Then compare the two lists and circle the factors that appear in both. Those are the common factors of the two numbers.
Practice Finding Factors and Common Factors
Finding factors becomes much easier when students have a systematic process instead of trying to pull multiplication facts from memory in random order. Working through the numbers in order helps students find all the factor pairs, while also reinforcing multiplication relationships, divisibility, and the connection between multiplication and division.
I’ve put together a free set of number cards you can use for practice. Students can choose one card and use the T-chart strategy to find all the factors of the number. To practice finding common factors, they simply choose two cards, find the factors of each number, and identify the factors the two numbers have in common. Because the numbers can be mixed and matched, the cards provide lots of practice without lots of prep.
The post Finding Factors and Common Factors appeared first on Math Coach's Corner.