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Flashcards · Maths · Number Without a Calculator

Factors, Multiples and Primes

18 cards

  1. What is a factor?

    A whole number that divides exactly into another number. The factors of 18 are 1, 2, 3, 6, 9 and 18.

  2. What is a multiple?

    A number in the times table of another number. The multiples of 7 are 7, 14, 21, 28 and so on.

  3. What is a prime number?

    A number with exactly two factors: 1 and itself.

  4. Is 1 a prime number? Is 2?

    1 is not prime because it has only one factor. 2 is prime, and it is the only even prime.

  5. What are the primes below 30?

    2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

  6. Why is 91 a trap in a prime question?

    It looks prime, but \(91 = 7 \times 13\).

  7. What is the divisibility test for 3 and 9?

    Add the digits. If the sum is a multiple of 3 (or 9), the number is divisible by 3 (or 9).

  8. How do you write 360 as a product of prime factors?

    Use a factor tree: \(360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 2^3 \times 3^2 \times 5\).

  9. How do you find the HCF from prime factors?

    Multiply the primes they share, taking the lower power of each.

  10. How do you find the LCM from prime factors?

    Multiply every prime that appears, taking the higher power of each.

  11. What is the HCF of 24 and 36?

    12, because \(24 = 2^3 \times 3\) and \(36 = 2^2 \times 3^2\).

  12. What is the LCM of 24 and 36?

    72, because it uses \(2^3 \times 3^2\).

  13. Which words in a question point to the HCF?

    ‘Greatest’ or ‘largest’ number that divides exactly into both, or sharing things into identical groups.

  14. Which words in a question point to the LCM?

    ‘Next time together’, ‘smallest number both go into’, or events that repeat at different intervals.

  15. How can you tell from prime factors that a number is a perfect square?

    Every index is even. \(36 = 2^2 \times 3^2\) is a square, but \(72 = 2^3 \times 3^2\) is not.

  16. What is the smallest number to multiply 72 by to get a square number?

    2, because \(72 \times 2 = 144 = 12^2\).

  17. How do you find \(\sqrt{2^2 \times 3^4}\)?

    Halve every index: \(2 \times 3^2 = 18\).

  18. How are the HCF, the LCM and the two numbers linked?

    HCF \(\times\) LCM equals the product of the two numbers. For 24 and 36: \(12 \times 72 = 24 \times 36 = 864\).