Understand factors, multiples, prime numbers, factorisation and divisibility.
A multiple of a number is obtained by multiplying it by a whole number; the multiples of 4 include 4, 8, 12, 16 and so on. A factor divides a number exactly, leaving no remainder. To find common multiples of two numbers, list multiples until shared values appear. To find common factors, list the factors of each number and identify those in both lists. Common multiples help with events that repeat at different intervals, while common factors help split collections into equal groups without leftovers.
A prime number has exactly two positive factors: 1 and itself. A composite number has more than two positive factors. The number 1 is neither prime nor composite because it has only one positive factor. Testing small divisors helps decide whether a number is prime, but checking every number up to the target is unnecessary: once a divisor larger than the square root would be needed, smaller divisors have already exposed any factor pair. For Class 6 work, systematic factor lists and divisibility tests are practical tools.
Two numbers are co-prime when their only common factor is 1. They do not both need to be prime: for example, 8 and 15 are co-prime because their factor lists share only 1. Conversely, two prime numbers are co-prime if they are different, while a number and itself share that number as a factor. In puzzles involving safe groupings or repeated arrangements, co-prime numbers have no larger common factor to use for a shared equal grouping. Check the common factors, rather than judging from the size of the numbers.
Prime factorisation expresses a composite number as a product of prime numbers. Repeatedly split a number into factors until every factor is prime. For example, 24 = 2×12 = 2×2×6 = 2×2×2×3. The same prime factors may be found in a factor tree arranged differently; what matters is the final prime product. Use multiplication to verify the result. Prime factorisation helps identify common factors and common multiples by showing which prime building blocks are shared and how often they occur.
Divisibility tests provide quick checks without carrying out long division. A whole number is divisible by 2 when its last digit is even; by 5 when it ends in 0 or 5; and by 10 when it ends in 0. For 3 and 9, add the digits and test whether the digit sum is divisible by 3 or 9. For 4, check whether the number formed by the last two digits is divisible by 4. Use the test that fits the divisor, and remember that a test tells divisibility, not necessarily the quotient.
Example 1: Factors of 12 are 1, 2, 3, 4, 6, 12; factors of 18 are 1, 2, 3, 6, 9, 18, so their common factors are 1, 2, 3, 6. Example 2: 30 = 2×3×5 is a prime factorisation. Example 3: 4,572 has digit sum 4+5+7+2 = 18, so it is divisible by 3 and 9. Common mistakes include calling 1 prime, treating every odd number as prime, stopping a factor tree before all leaves are prime, or confusing a multiple with a factor. Verify products and test the stated divisor.
| Idea | How to use it | Check |
|---|---|---|
| Identify the rule | Describe what changes and what remains fixed. | Test more than one example. |
| Choose a representation | Use a diagram, number line, table or equation. | Labels and units are clear. |
| Explain the answer | Show the operation and each step. | The result fits the question. |
Example A. Read the question and name the relevant mathematical idea. Write the information given before choosing an operation. This prevents a familiar-looking number from being used in the wrong way.
Example B. Show the calculation in small steps. For example, when a calculation involves a product and a sum, compute the product first if the expression requires it, then add. Keep intermediate values visible so an arithmetic slip can be found.
Example C. Check the result using a second representation where possible: estimate it, draw a model, use a number line, or substitute it back into the original relationship. A check is especially useful when a question involves units, scale, direction or a geometric condition.
No; it has only one positive factor.
A number that divides another exactly.
Expressing a number as a product of prime numbers.
Add the digits and check if the sum is divisible by 9.
Prime Time builds mathematical understanding through careful observation and clear representations. Identify the key quantities, shapes or relationships before choosing a method. Use diagrams, tables, number lines or equations to make thinking visible. Show calculations in order and keep labels and units consistent. Check whether the result satisfies the definition or rule in the question. Explain the result in a sentence so another learner can follow the reasoning.