PSHS NCE Factors, Multiples, and Divisibility Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Factors, Multiples, and Divisibility

Find number patterns faster, recognize what divides evenly, and know when to use factors, multiples, GCF, or LCM.

Grade 6–7 friendly Fast divisibility tricks Regular practice Quick Fire + Mastery

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Factors, Multiples, and Divisibility

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Factors go in. Multiples come out.

4 × 6 = 24

4 and 6 are factors of 24. They divide 24 evenly.

24 is a multiple of 4 and 6.

Think of it this way:
Factors are numbers that can fit evenly into a number.
Multiples are answers you get when you keep multiplying.

Factors of 12
1, 2, 3, 4, 6, 12

Multiples of 12
12, 24, 36, 48, 60...

DO IT FAST

Know what the question is asking

1. “Divides evenly?” Think factor or divisibility.
2. “What comes next?” Think multiples.
3. “Greatest number that divides both?” Think GCF.
4. “First number both can reach?” Think LCM.

Fast divisibility checks:
2 → last digit is even
3 → digit sum is divisible by 3
5 → ends in 0 or 5
9 → digit sum is divisible by 9
10 → ends in 0

WORKED EXAMPLES

Six patterns you should recognize

1. Is it a factor?

Is 6 a factor of 42?

42 ÷ 6 = 7

Yes. There is no remainder.

2. Is it a multiple?

Is 45 a multiple of 9?

9 × 5 = 45

Yes.

3. Divisible by 3

Is 7,245 divisible by 3?

7 + 2 + 4 + 5 = 18

Yes. 18 is divisible by 3.

4. Prime or composite?

Is 29 prime?

The only factors are 1 and 29.

29 is prime.

5. Greatest common factor

Find the GCF of 18 and 24.

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

GCF = 6.

6. Least common multiple

Find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16...
Multiples of 6: 6, 12, 18...

LCM = 12.

TRY WITH ME

Do we need GCF or LCM?

Two lights blink every 6 seconds and every 8 seconds. If they blink together now, after how many seconds will they blink together again?

1. We need a number that both 6 and 8 can reach.
2. That means we need a common multiple.
3. We want the first one, so we need the least common multiple.

Multiples of 6: 6, 12, 18, 24...
Multiples of 8: 8, 16, 24...
Answer: 24 seconds.

COMMON TRAPS

Watch out for these

Mixing up factors and multiples.
Factors are limited. Multiples keep going.

Using LCM when the problem asks for biggest equal groups.
That usually needs GCF.

Calling 1 a prime number.
Prime numbers have exactly two factors. The number 1 has only one.

Doing long division when a divisibility rule is faster.
Check the digits first.

REGULAR PRACTICE

Build the skill

These mix factors, multiples, divisibility, prime numbers, GCF, and LCM.

QUICK FIRE

Can you spot it fast?

Five short questions. Use the fastest valid method.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Not sure whether a problem needs GCF or LCM?

Send Teacher Abi the question that confused you and your result. I can help you spot the clue faster.

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