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Every whole number can be described by its factors:

• Even numbers are divisible by 2 (2, 4, 6, 8 …); odd numbers are not (1, 3, 5, 7 …).
• Prime numbers have exactly two factors — 1 and the number itself (2, 3, 5, 7, 11 …).
• Composite numbers have more than two factors (4, 6, 8, 9 …).

Factors and multiples are two sides of the same coin:

• A factor divides a number exactly, with no remainder. 3 is a factor of 12 because 12 ÷ 3 = 4.
• A multiple is what you get by multiplying. 12 is a multiple of 3 because 3 × 4 = 12.
• So whenever 3 is a factor of 12, the number 12 is a multiple of 3 — the relationship works both ways.

The factors of 12 are 1, 2, 3, 4, 6 and 12. The multiples of 3 are 3, 6, 9, 12, 15 … — factors are divided into, multiples are built up from.

Numbers hide all sorts of patterns once you start playing with them:

• A palindrome reads the same forwards and backwards — like 121 or 1331. Reverse the digits and you get the same number.
• Adding odd numbers in order makes perfect squares: 1, 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16 …
• Try the reverse-and-add trick: take 27, add its reverse 72 → 99, a palindrome!

Spotting these patterns turns arithmetic into a game — and trains you to look for structure everywhere.