Find Common Factors in Lists

Teaching Notes

Focus: Common Factors and Greatest Common Factor. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Use multiplication and division facts.

Teaching Steps for Parents and Teachers

1. Factors divide a number with no remainder.
2. Multiples are products of the number and whole numbers.
3. For common factors or multiples, compare the lists for both numbers.

Worked Examples

Find the greatest common factor of 12 and 18.

1. Factors of 12: 1, 2, 3, 4, 6, 12.
2. Factors of 18: 1, 2, 3, 6, 9, 18.
3. The greatest number in both lists is 6.

Answer: 6

Common Mistakes and How to Help

Factors and multiples are different kinds of lists.

Does 6 divide both numbers without a remainder?

Questions to Check Understanding

• Does 6 divide both numbers without a remainder?
• Which step explains your answer?
• Can you apply the same reasoning when the numbers change?

Practice Advice

Work through the example together. Ask the learner to explain the first two problems, then try three independently. Review the first incorrect step before assigning more practice.

Next Practice

• Use New Numbers to practice the same skill with different values.
• If the learner needs help, return to the example and model each step before trying again.