Last reviewed: 7 November 2026
Updated November 2026. These Grade 7 factors notes cover divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10 and 11, writing composite numbers as a product of prime factors, and finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) by the factor method. Quick example: 36 = 2² × 3² and 60 = 2² × 3 × 5, so GCD = 2² × 3 = 12 and LCM = 2² × 3² × 5 = 180.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 7 maths topics, see our Grade 7 mathematics revision guide and the Grade 7 notes hub.
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What the Grade 7 Curriculum Covers
Factors is a sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 7 Mathematics design. Learners test divisibility by 2, 3, 4, 5, 6, 8, 9, 10 and 11, express composite numbers as a product of prime factors, and work out and apply the GCD and LCM by the factor method. The design is listed on the KICD Grade Seven curriculum designs page.
Divisibility Tests
| Divisible by | Test | Example |
|---|---|---|
| 2 | Last digit is even | 3,586 |
| 3 | Sum of digits divisible by 3 | 471: 4 + 7 + 1 = 12 |
| 4 | Last two digits divisible by 4 | 9,324: 24 ÷ 4 = 6 |
| 5 | Last digit 0 or 5 | 8,405 |
| 6 | Divisible by both 2 and 3 | 1,242: even, and 1 + 2 + 4 + 2 = 9 |
| 8 | Last three digits divisible by 8 | 2,376: 376 ÷ 8 = 47 |
| 9 | Sum of digits divisible by 9 | 2,376: 2 + 3 + 7 + 6 = 18 |
| 10 | Last digit is 0 | 7,850 |
| 11 | Alternating sum of digits is 0 or divisible by 11 | 2,376: 2 − 3 + 7 − 6 = 0 |
So 2,376 passes the tests for 2, 3, 4, 6, 8, 9 and 11, but not 5 or 10.
Prime and Composite Numbers
A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11, 13 …). A composite number has more than two factors. 1 is neither prime nor composite. Every composite number can be written as a product of primes, as shown in OpenStax Prealgebra’s section on prime factorisation and the least common multiple.
Worked example: prime factors of 360
Divide repeatedly by the smallest prime that works: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1. So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
GCD by the Factor Method
The GCD is the largest number that divides all the given numbers. Write each in prime factors and multiply the primes they share, using the lowest power of each.
Example: 48 = 2⁴ × 3 and 72 = 2³ × 3². Shared: 2³ and 3. GCD = 8 × 3 = 24.
LCM by the Factor Method
The LCM is the smallest number that all the given numbers divide into. Multiply every prime that appears, using the highest power of each.
Example: 12 = 2² × 3 and 18 = 2 × 3². LCM = 2² × 3² = 36.
Using GCD and LCM in Real Life
GCD problems ask for the biggest equal pieces or groups. Two ribbons are 48 cm and 72 cm long and are cut into equal pieces as long as possible with nothing left over: the longest piece is GCD(48, 72) = 24 cm.
LCM problems ask when things happen together again. One school bell rings every 12 minutes and another every 18 minutes. If they ring together at 8:00 a.m., they next ring together after LCM(12, 18) = 36 minutes, at 8:36 a.m.
A useful check: for two numbers, GCD × LCM = the product of the numbers. 24 × LCM(48, 72) should equal 48 × 72 = 3,456, so LCM(48, 72) = 144.
Original Practice Questions With Worked Answers
- Is 5,148 divisible by 4 and by 9? 48 ÷ 4 = 12, yes. 5 + 1 + 4 + 8 = 18, yes.
- Is 7,392 divisible by 11? 7 − 3 + 9 − 2 = 11, so yes.
- Write 252 as a product of prime factors. 2² × 3² × 7.
- Find the GCD and LCM of 30 and 45. 30 = 2 × 3 × 5; 45 = 3² × 5. GCD = 15; LCM = 90.
- Buses leave every 15 and 20 minutes from the same stage, together at 6:00 a.m. When do they next leave together? LCM = 60 minutes, so 7:00 a.m.
Cover the answers and attempt each question first. For timed practice, use the Grade 7 revision papers or the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the divisibility test for 11?
Alternately add and subtract the digits from left to right. If the result is 0 or divisible by 11, the number is divisible by 11.
What is the difference between GCD and LCM?
The GCD is the largest number that divides all the given numbers. The LCM is the smallest number that all the given numbers divide into.
How do you find the GCD using prime factors?
Write each number as a product of primes and multiply the common primes, using the lowest power of each.
Is 1 a prime number?
No. A prime number has exactly two different factors, and 1 has only one.