A factor pair is a pair of numbers that when multiplied together, give you the original number. For example, the factor pairs of 12 are (1, 12), (2, 6), and (3, 4).
To find the factor pairs of a number, you can start by dividing the number by 2 and then continue dividing by integers until the number is no longer divisible by that integer. For example, to find the factor pairs of 12:
- Divide 12 by 2: 12 ÷ 2 = 6
- Divide 12 by 3: 12 ÷ 3 = 4
- Divide 12 by 4: 12 ÷ 4 = 3 (not a whole number, so stop)
The factor pairs of 12 are (1, 12), (2, 6), and (3, 4)
You can also use a factor tree to find the factor pairs of a number. A factor tree is a diagram that shows the prime factorization of a number. The leaves of the tree are the prime factors of the number, and the branches are the non-prime factors. To use a factor tree, you can start by dividing the number by the smallest prime number that divides it. For example, to find the factor pairs of 12:
- Draw a box with the number 12 inside
- Draw a line from the box, dividing it into two smaller boxes. Write 2 in one box and 6 in the other.
- Draw a line from the 6 box, dividing it into two smaller boxes. Write 2 in one box and 3 in the other.
The factor pairs of 12 are (1, 12), (2, 6), and (3, 4).
Let’s say you have the number 18. To find the factor pairs of 18, you can start by dividing it by 2 and then continue dividing by integers until the number is no longer divisible by that integer:
- Divide 18 by 2: 18 ÷ 2 = 9
- Divide 18 by 3: 18 ÷ 3 = 6
- Divide 18 by 4: 18 ÷ 4 = 4.5 (not a whole number, so stop)
The factor pairs of 18 are (1, 18), (2, 9), and (3, 6)
You can also use a factor tree to find the factor pairs of 18:
- Draw a box with the number 18 inside
- Draw a line from the box, dividing it into two smaller boxes. Write 2 in one box and 9 in the other.
- Draw a line from the 9 box, dividing it into two smaller boxes. Write 3 in one box and 3 in the other.
The factor pairs of 18 are (1, 18), (2, 9), and (3, 6)
So, in this example, the factor pairs of 18 are (1, 18), (2, 9), and (3, 6).
It’s important to notice that the pairs (2,9) and (3,6) are the pairs that when multiplied yield 18, and (1,18) is always a factor pair of any number.
Another way of finding factor pair
In Year 4 Math, a factor pair is a pair of numbers that when multiplied together, equal a given number. To find the factor pairs of a number, you can use the following steps:
- Write down the number you want to find the factor pairs of.
- Start with the number 1 and divide the number by 1. Write down the quotient and the remainder.
- Move on to the number 2 and divide the number by 2. Write down the quotient and the remainder.
- Continue this process with numbers 3, 4, 5, and so on, until you reach the square root of the number.
- For each quotient and remainder, if the remainder is 0, then the quotient and the number you divided by (the divisor) are a factor pair.
For example, to find the factor pairs of the number 12:
- Start with 1: 12 ÷ 1 = 12 remainder 0, so (1, 12) is a factor pair.
- Move on to 2: 12 ÷ 2 = 6 remainder 0, so (2, 6) is a factor pair.
- Move on to 3: 12 ÷ 3 = 4 remainder 0, so (3, 4) is a factor pair.
- The square root of 12 is 3.46, so we don’t need to continue any further.
The factor pairs of 12 are (1, 12), (2, 6), and (3, 4).
It’s also important to note that when finding the factor pairs, if the quotient and divisor are the same number then that is a perfect square.
Online Tests
Year 4 Math: Unit 3. Multiplication & division- Worksheets – Printable
- Factor Pairs – Worksheets -1
- Factor Pairs – Worksheets -2
- Factor-pairs-reasoning and problem-Worksheets
- Multiply-by-10 – Worksheets -1
- Multiply-by-100 – Worksheets -1
- Multiply By 10 Reasoning and Problem Solving
- Year 4 Multiply by 100 Varied Fluency
- Year 4 Multiply By 100 Reasoning and Problem Solving
- Challenge-Multiply-by-10
- Challenge-Multiply-by-100
- Efficient multiplication
- Related facts – multiplication and division
- Informal written methods for multiplication
- Multiply a 2-digit number by a 1-digit number
- Multiply a 3-digit number by a 1-digit number
- Multiply 3 digits
- Multiplication using Pictures
- Multiplying Whole Numbers up to 10
- Horizontal Multiplication Drill | Factors up to 10
- Single-Digit Multiplication Word Problems
- Completing Multiplication Equations | Number Lines
- Partially-Filled Multiplication Charts
- Balancing Multiplication Equations
- Forming Product
- Horizontal Multiplication Facts
- Multiplication Display Chart 1 to 15
- Challenge-Multiply-by-10
- Challenge-Multiply-by-100
- divide-by-10 -Worksheets -1
- divide-by-100 – Worksheets -1
- Year 4 Divide by 10 Varied Fluency
- Year 4 Divide by 10 Reasoning and Problem Solving
- Year 4 Divide by 100 Varied Fluency
- Year 4 Divide by 100 Reasoning and Problem Solving
- Divide a 2-digit number by a 1-digit number
- Divide a 2-digit number by a 1-digit number-2
- Divide a 3-digit number by a 1-digit number
- Correspondence problems
- Division Tables Chart | 12-in-1 Page
- Equivalent Division Sentences | Number Line Models
- Division Facts for 5
- Standard Division | Without Remainder
- Division Models | Equal Groups
- Representing Division in 3 Models | Activity
- Drawing Hops on the Number Line Models
- Writing Division Sentences | Arrays
- Division by Single-Digit Divisors Standard
- Division and Unit Price
- Division Word Problems
- Completing Out Boxes
- Multiplication and Division Fact Families
- Completing Fact Families | Missing Numbers
- Division Area Models
- Writing Division Sentences | Drawing Equal Groups
- Array Division Word Problems
- Division Riddles
- 2-Digit Dividends by 1-Digit Divisors | Without Remainder
- Two-Digit by Single-Digit Division | Word Problems
- Division Riddles | Single-Digit and 2-Digit Quotients
- Challenge-Divide by 10
- Challenge-Divide by 100
- Challenge-Divide by 10