Patterns in Factors & Multiples

18 → 1 + 8 = ___

27 → 2 + 7 = ___

36 → 3 + 6 = ___

45 → 4 + 5 = ___

What pattern do you notice? ___

Multiples of 4: ___, ___, ___, ___, ___ | Multiples of 6: ___, ___, ___, ___, ___. Common multiples: ___

Multiples of 3: ___, ___, ___, ___, ___ | Multiples of 5: ___, ___, ___, ___, ___. Common multiples: ___

Multiples of 6: ___ Multiples of 8: ___ Common multiples: ___

Multiples of 5: ___ Multiples of 7: ___ Common multiples: ___

Is 126 divisible by 2? ___ By 3? ___ By 6? ___

Is 255 divisible by 3? ___ By 5? ___ By 9? ___

Is 840 divisible by 2? ___ By 3? ___ By 5? ___ By 10? ___

Is 378 divisible by 2? ___ By 3? ___ By 9? ___

Is 450 divisible by 2? ___ By 5? ___ By 9? ___ By 10? ___

Is 693 divisible by 3? ___ By 7? ___ By 9? ___

Step 1: ___

Step 2: ___

Step 3: ___

Test your algorithm on 42: ___

Test your algorithm on 35: ___

Step 1: Check if the number is divisible by ___

Step 2: Check if the number is divisible by ___

Step 3: If BOTH are true, then ___

Test on 54: ___

Test on 40: ___

Factors of 12: ___. Factors of 18: ___. HCF: ___

Factors of 24: ___. Factors of 36: ___. HCF: ___

Factors of 20: ___. Factors of 30: ___. HCF: ___

Write all numbers from 1–30 that are multiples of BOTH 2 and 3: ___

What do you notice about these numbers? They are all multiples of ___

Write all numbers from 1–50 that are multiples of BOTH 3 and 5: ___

What is the pattern? ___

I am between 40 and 60. I am a multiple of 7. I am also a multiple of 3. What am I?

I am a two-digit number. All my factors are odd. My digits add up to 10. What could I be?

Factors of 18: ___

Factors of 36: ___

Factors of 20: ___

Factors of 48: ___

Factors of 40: ___

Factors of 50: ___

Factors of 60: ___

Factors of 100: ___

Multiples of 6: ___

Multiples of 9: ___

Multiples of 12: ___

Multiples of 15: ___

Common factors of 12 and 18: ___. HCF: ___

Common factors of 20 and 30: ___. HCF: ___

Common factors of 24 and 36: ___. HCF: ___

Common multiples of 4 and 6: ___. LCM: ___

Common multiples of 3 and 5: ___. LCM: ___

Common multiples of 6 and 8: ___. LCM: ___

12 = ___ × ___ × ___

18 = ___ × ___ × ___

30 = ___ × ___ × ___

48 = ___ × ___ × ___ × ___

Factor tree for 36:

Factor tree for 60:

Hotdog buns come in packs of 6. Sausages in packs of 8. What is the smallest number where you have equal amounts? (LCM)

You have 24 red beads and 36 blue beads. What is the largest number of identical groups you can make? (HCF)

I am the smallest number with exactly 6 factors. What am I? Show the factors.

I am a 2-digit prime number. My digits add to 8. I am less than 50. What could I be? (list all)

72 = ___ × ___ = ___ × ___ × ___ × ___ (prime factors)

100 = ___ × ___ = ___ × ___ × ___ (prime factors)

What is the HCF of 72 and 100? Use the prime factors:

Lily visits the library every 4 days. Noah every 6 days. When do they both visit on the same day? ___

A baker has 24 blueberry and 36 chocolate muffins. What is the maximum number of identical boxes? ___

Was this an LCM or HCF problem? Explain:

List multiples of 4 up to 40: ___

List multiples of 6 up to 40: ___

List the numbers that are multiples of BOTH 4 and 6 (put in the overlap): ___

The LCM of 4 and 6 is: ___

Why do computers use prime numbers for security (encryption)?

The Cicada Periodical Cicada lives underground for 13 or 17 years (both prime). Why might this help cicadas survive?

List all twin primes (primes differing by 2) up to 50:

Traffic lights cycle: Light A every 40 s, Light B every 60 s. After how many seconds are they both green together? ___

Bus routes: Route 1 every 12 min, Route 2 every 8 min. After how many minutes do they depart at the same time?

80 red balloons and 60 blue balloons are divided into equal bunches with no leftover. Max bunch size: ___

144 apples and 108 oranges in identical boxes. Each box has all one type. Max apples per box: ___ Max oranges: ___

Factors of 12 (excluding 12): 1+2+3+4+6 = ___. Is 12 abundant? ___

Factors of 8 (excluding 8): 1+2+4 = ___. Is 8 abundant or deficient? ___

Find another abundant number less than 20: ___

I am a 3-digit number. I am a multiple of 9. My digits sum to 18. I am between 400 and 500. What could I be? ___

I am the HCF of 48, 60 and 84. What am I? ___

Circle 2. Cross out all multiples of 2. Now circle 3 and cross its multiples. Continue with 5 and 7. List primes: ___

How many prime numbers are there between 1 and 50? ___

Factor tree for 72: ___. Prime factorisation: ___

Factor tree for 120: ___. Prime factorisation: ___

HCF of 72 and 120 using prime factors: ___

List the first 5 multiples of 6: ___. First 5 multiples of 8: ___.

Circle the common multiples. What is the LCM? ___

How is the LCM related to the product of the two numbers? 6 × 8 = 48. LCM = 24. Relationship: ___

10 = ___ + ___. 16 = ___ + ___. 28 = ___ + ___

Is this always true for all even numbers you can try? ___. Test with 42 = ___ + ___

Start from 1 and work up: Factors of 72 = ___

Check in pairs: 1×72, 2×36, 3×24... Factors of 72 in pairs: ___

Why is working in pairs more efficient? ___

List all factor pairs of 120: ___

How many factors does 120 have? ___

Find two numbers less than 50 that have exactly 8 factors: ___

Cross out all multiples of 2 (except 2) from 2 to 50. List remaining numbers: ___

Now cross out multiples of 3, 5 and 7. What numbers are left? These are primes: ___

How many prime numbers are between 1 and 50? ___

Factor tree for 72:

Factor tree for 84:

Factor tree for 90:

Write all numbers from 1–100 divisible by BOTH 4 and 6: ___

These are all multiples of ___

Generalise: if a number is divisible by both a and b, it is divisible by ___

I have exactly 4 prime factors (not necessarily different). I am less than 100. What could I be? (List all possibilities)

I am a prime number between 70 and 90. What are my possibilities?

Describe a step-by-step method (algorithm) for deciding whether a number is prime.

Test your algorithm on 97. Is it prime? ___

Write an algorithm to find all common multiples of two numbers up to 100.

Apply your algorithm to find common multiples of 7 and 11 up to 100: ___