Types of Numbers | Functional Skills Maths Level 2

Learning Objectives

Identify odd and even numbers
Define and identify integers and whole numbers
Find factors and multiples of numbers
Identify prime numbers
Recognise square numbers and cube numbers

Real-World Applications

Finance: Interest rates and loan periods are always whole numbers or integers — no fractions allowed.
Construction: Prime numbers appear in gear ratios to avoid repeated meshing patterns.
Data: Square numbers arise naturally in area calculations; a 5 m × 5 m room is \(5^2 = 25\) m².

How Do You Tell If a Number Is Odd or Even?

Every whole number is either odd or even, and you can tell which just by looking at its last digit. A number ending in 0, 2, 4, 6 or 8 is even; a number ending in 1, 3, 5, 7 or 9 is odd — the rest of the digits don't matter.

Even numbers

Divisible by 2 — no remainder.

Last digit: 0, 2, 4, 6 or 8

Examples: 2, 4, 18, 56, 100, 374

Odd numbers

Not divisible by 2 — always leaves remainder 1.

Last digit: 1, 3, 5, 7 or 9

Examples: 1, 3, 17, 45, 99, 237

Even + Even = Even | Odd + Odd = Even | Odd + Even = Odd
Even × Even = Even | Odd × Odd = Odd | Odd × Even = Even

Example — Is 4,736 odd or even?

Step 1

Look only at the last digit: 6

Step 2

6 ends in an even digit → 4,736 is even

Example — Without calculating, is \(17 \times 9\) odd or even?

Step 1

17 is odd, 9 is odd

Step 2

Odd × Odd = Odd → the answer will be odd (it is 153)

⚠ Watch out: Zero is an even number — it is divisible by 2 with no remainder. A common mistake is to think zero is neither odd nor even.

✓ Quick Check 1 — Odd and Even Numbers

Question 1 of 5

Integers and Whole Numbers

Numbers can be grouped by what they include. Understanding the difference between whole numbers and integers helps you answer questions correctly.

Whole numbers are 0, 1, 2, 3, 4, … — no negatives, no decimals.
Integers include all whole numbers and their negative counterparts: …, −3, −2, −1, 0, 1, 2, 3, … — positive, negative, and zero, but no decimals or fractions.

Example 1 — Is each number a whole number, an integer, or neither?

Step 1

\(-7\) is negative — it is an integer but NOT a whole number (whole numbers start at 0).

Step 2

\(0\) is zero — it is both a whole number and an integer.

Step 3

\(4\) is a positive counting number — it is both a whole number and an integer.

Step 4

\(2.5\) is a decimal — it is neither (integers and whole numbers cannot have decimal parts).

Example 2 — Is \(-15\) an integer? Is \(-15\) a whole number?

Step 1

\(-15\) is negative → YES, it is an integer (integers include negatives).

Step 2

\(-15\) is negative → NO, it is NOT a whole number (whole numbers are 0, 1, 2, 3, … only).

✓ Quick Check 1b — Integers and Whole Numbers

Question 1 of 10

Factors, Multiples and Prime Numbers

Factor: a number that divides exactly into another. Factors of 12: 1, 2, 3, 4, 6, 12.
Multiple: the result of multiplying a number by an integer. Multiples of 5: 5, 10, 15, 20, …
Prime: has exactly 2 factors (1 and itself). Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Not prime: any number with more than 2 factors. Examples: 4, 6, 8, 9, 10, 12…
Special case: 1 is NOT a prime number (it only has one factor — itself).

Example 3 — Find all factors of 36

Step 1

Start from 1 and work up: \(1 \times 36,\; 2 \times 18,\; 3 \times 12,\; 4 \times 9,\; 6 \times 6\)

Step 2

Stop when you reach the square root (\(\sqrt{36} = 6\)).

Step 3

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Example 4 — Is 51 prime?

Step 1

Check divisibility: \(51 \div 2 = 25.5\) (no), \(51 \div 3 = 17\) (yes!).

Step 2

Since \(51 = 3 \times 17\), it has more than 2 factors.

Step 3

51 is NOT a prime number — it has more than 2 factors.

✓ Quick Check 2 — Factors, Multiples and Primes

Question 1 of 10

Square Numbers and Cube Numbers

Special sequences of numbers appear throughout maths. Recognising them instantly saves time in the exam.

Type	Sequence	Note
Square numbers	1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144	\(n^2\)
Cube numbers	1, 8, 27, 64, 125, 216	\(n^3\)

Example 5 — Evaluate \(\sqrt{144}\)

Step 1

Ask "which number squared gives 144?"

Step 2

\(10^2 = 100,\quad 12^2 = 144\) → Answer: \(\sqrt{144} = 12\)

Step 3

Check: \(12 \times 12 = 144\) ✓

Example 6 — Is 72 a cube number?

Step 1

List cube numbers: 1, 8, 27, 64, 125…

Step 2

\(4^3 = 64,\quad 5^3 = 125\) — 72 is between these.

Step 3

72 is NOT a cube number.

✓ Quick Check 3 — Square and Cube Numbers

Question 1 of 10

Practice: Types of Numbers

Answer each question, then click Check All.

#	Question	Answer	Result
1	Is −6 an integer? (yes or no)
2	List the first 5 multiples of 7
3	What is 8² (8 squared)?
4	Is 37 prime? (yes or no)
5	What is √81?
6	Find all factors of 20
7	What is 4³ (4 cubed)?
8	What is \(3^3\) (3 cubed)?
9	Is 51 prime? (yes or no)
10	What is 5² (5 squared)?

⚠ Things to Watch Out For

Confusing factors and multiples: Factors of 12 are numbers that divide INTO 12 (1,2,3,4,6,12). Multiples of 12 are 12×1, 12×2 etc. These are opposite ideas.
Is 1 a prime number? No — prime numbers must have exactly two factors: 1 and themselves. 1 only has one factor, so it is not prime.
Is 2 prime? Yes — 2 is the only even prime number. All other even numbers have 2 as a factor, giving them more than 2 factors, so they are not prime.
Square vs square root: 4² = 16, but √16 = 4. Students often confuse squaring with finding the square root.
Negative square roots: √9 = 3 (the positive root). At FS2 level, square roots are always the positive value.

What would you like to do next?