Find factors of numbers up to 100

What you will learn

• Find factors of numbers up to 100

Models used: number sentences, stories, tables.

Which rows fit exactly?

Try arranging 12 counters in rows of 3. There are no leftovers.

1. 4 rows run across the picture; each row contains 3 objects.

   Try arranging 12 counters in rows of 3. There are no leftovers.

   A factor fits exactly. Factor pairs record the two whole numbers whose product is the total.

   4 rows of 3 = 4 × 3 = 12

2. 3 rows run across the picture; each row contains 4 objects.

   So 3 and 4 are both factors of 12: they make a complete rectangle.

   3 × 4 = 12

   3 rows of 4 = 3 × 4 = 12

3. Each bag is one group. Counters outside the bags are left over.

   Rows of 5 leave 2 counters outside. Five is not a factor of 12.

   Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.

   Group 1: 5

   Group 2: 5

Worked example: A new example, together

Which number is a factor of 30?

1. A product links factors and multiples. Read each value with the heading above its column.

   Match each proposed group size with the number of complete groups it makes.

   A factor divides a amount into complete equal groups.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

2. A product links factors and multiples. Read each value with the heading above its column.

   List factor pairs by testing exact division.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

   Which number is a factor of 30?

   6

3. A product links factors and multiples. Read each value with the heading above its column.

   List factor pairs by testing exact division.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

4. A product links factors and multiples. Read each value with the heading above its column.

   A common factor must divide both given numbers.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

5. A product links factors and multiples. Read each value with the heading above its column.

   30 ÷ 6 = 5, with no remainder.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

6. A product links factors and multiples. Read each value with the heading above its column.

   Check the result against the question we started with.

   6 × 5 = 30.

   We found 6. A factor divides a amount into complete equal groups.

   A product links factors and multiples

   Number	Some factor pairs
   30	1 × 30; 6 × 5

Common mistakes to discuss

• Every smaller number is a factor. A factor leaves no remainder. 5 is not a factor of 12, because 12 ÷ 5 leaves 2.

Check your understanding

• Find factors of numbers up to 100
• justify a factor or common factor with exact grouping
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.