Factors
4A · Chapter 3 · Lesson 3 · MATH-4A-C03-L03
Learning goal. List factor pairs systematically using division and rectangular arrays.
Before you begin
Recall: Grade 3: arrays and multiplication tables; 4A Ch2: addition strategies; Common Multiples. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Will 288 be a common multiple of 16 and 9? Explain.
Show answer & reasoning
288 is two times their least common multiple, so both numbers divide it.
Find the least positive common multiple of 9 and 16.
Show answer & reasoning
List positive multiples of each or use prime factors to locate the first shared positive multiple: 144.
Find the least positive common multiple of 12 and 9.
Show answer & reasoning
List positive multiples of each or use prime factors to locate the first shared positive multiple: 36.
Key vocabulary
- multiple
- whole-number product of a given number
- factor
- whole number dividing exactly
- prime
- positive number with exactly two positive factors
- composite
- positive number with more than two positive factors
Understand the concept
Factors divide a positive whole number without leaving a remainder. Rectangular arrays show factor pairs: twelve counters make 1×12, 2×6, or 3×4 rectangles. List pairs systematically to avoid missing divisors. Unlike multiples, the positive factors of a number form a finite list.
Model it: array grids and factor pair chart. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
List all positive factors of 80.
Each factor divides 80 with no remainder; pair divisors with their matching quotients.
Check your understanding 1
List all positive factors of 108.
Show answer & reasoning
Each factor divides 108 with no remainder; pair divisors with their matching quotients.
Worked example 2
List all positive factors of 56.
Each factor divides 56 with no remainder; pair divisors with their matching quotients.
Check your understanding 2
List all positive factors of 40.
Show answer & reasoning
Each factor divides 40 with no remainder; pair divisors with their matching quotients.
Worked example 3
List all positive factors of 150.
Each factor divides 150 with no remainder; pair divisors with their matching quotients.
Check your understanding 3
List all positive factors of 72.
Show answer & reasoning
Each factor divides 72 with no remainder; pair divisors with their matching quotients.
Guided practice
List all positive factors of 35.
Show answer & reasoning
Each factor divides 35 with no remainder; pair divisors with their matching quotients.
List all positive factors of 49.
Show answer & reasoning
Each factor divides 49 with no remainder; pair divisors with their matching quotients.
List all positive factors of 144.
Show answer & reasoning
Each factor divides 144 with no remainder; pair divisors with their matching quotients.
List all positive factors of 130.
Show answer & reasoning
Each factor divides 130 with no remainder; pair divisors with their matching quotients.
Is 7 a factor of 28? Give a reason.
Show answer & reasoning
28 ÷ 7 = 4, a whole number.
Independent practice
List all positive factors of 99.
Show answer & reasoning
Each factor divides 99 with no remainder; pair divisors with their matching quotients.
List all positive factors of 20.
Show answer & reasoning
Each factor divides 20 with no remainder; pair divisors with their matching quotients.
List all positive factors of 63.
Show answer & reasoning
Each factor divides 63 with no remainder; pair divisors with their matching quotients.
Is 13 a factor of 65? Give a reason.
Show answer & reasoning
65 ÷ 13 = 5, a whole number.
Is 4 a factor of 40? Give a reason.
Show answer & reasoning
40 ÷ 4 = 10, a whole number.
List all positive factors of 135.
Show answer & reasoning
Each factor divides 135 with no remainder; pair divisors with their matching quotients.
List all positive factors of 120.
Show answer & reasoning
Each factor divides 120 with no remainder; pair divisors with their matching quotients.
List all positive factors of 84.
Show answer & reasoning
Each factor divides 84 with no remainder; pair divisors with their matching quotients.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A learner says 12 has only factors 2, 3, and 4. Explain the omitted factors and list all positive factors.
Show answer & reasoning
Factor pairs of 12 are (1,12), (2,6), and (3,4).
List all positive factors of 48.
Show answer & reasoning
Each factor divides 48 with no remainder; pair divisors with their matching quotients.
Exit check
List all positive factors of 64.
Show answer & reasoning
Each factor divides 64 with no remainder; pair divisors with their matching quotients.
Is 14 a factor of 126? Give a reason.
Show answer & reasoning
126 ÷ 14 = 9, a whole number.
Is 8 a factor of 104? Give a reason.
Show answer & reasoning
104 ÷ 8 = 13, a whole number.