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Understanding factors, multiples, and prime numbers is important for the CSSE maths paper. These concepts help you simplify fractions, find common denominators, and solve a wide range of number problems. Let us work through each topic carefully.
Factors of a number are whole numbers that divide into it exactly, with no remainder.
Work in pairs. Start with 1 × the number itself, then try 2, 3, 4... and stop when the pairs meet or cross.
Find all factors of 36.
| Pair | Product |
|---|---|
| 1 × 36 | 36 |
| 2 × 18 | 36 |
| 3 × 12 | 36 |
| 4 × 9 | 36 |
| 6 × 6 | 36 |
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 (that is 9 factors in total).
Top Tip: Factor pairs are a neat way to make sure you never miss one. Always start from 1 and work upwards.
Multiples of a number are found by multiplying that number by 1, 2, 3, 4, 5 and so on. They form the times table for that number.
A number is a multiple of another if it divides exactly with no remainder.
Common factors are factors that two or more numbers share.
The Highest Common Factor (HCF) is the largest common factor.
Find the HCF of 24 and 36.
Why is the HCF useful? You use it to simplify fractions. To simplify 24/36, divide both by the HCF (12): 24/36 = 2/3.
Common multiples are multiples that two or more numbers share.
The Lowest Common Multiple (LCM) is the smallest common multiple.
Find the LCM of 6 and 8.
Why is the LCM useful? You use it to find a common denominator when adding or subtracting fractions. For 1/6 + 1/8, the common denominator is 24.
A prime number has exactly two factors: 1 and itself.
Prime numbers up to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
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