1.5 Factors, multiples and prime numbers
9 exam questions worth 18 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Which of these numbers is a prime number?
Choose one answer.
Correct Not quite: the answer is 59
Mark scheme
C: 59
Model answer
59 (C). 51 = 3 × 17, 57 = 3 × 19 and 63 = 7 × 9, but 59 has no factors other than 1 and 59.
List all the factors of 30.
Mark scheme
M1: at least four correct factors; A1: 1, 2, 3, 5, 6, 10, 15, 30 (no extras)
Model answer
1 × 30, 2 × 15, 3 × 10, 5 × 6, so the factors are 1, 2, 3, 5, 6, 10, 15 and 30.
Write down the first five multiples of 7.
Mark scheme
B1: 7, 14, 21, 28, 35
Model answer
7, 14, 21, 28, 35.
Write down the common factors of 18 and 27.
Mark scheme
M1: list of factors of both numbers (1, 2, 3, 6, 9, 18 and 1, 3, 9, 27); A1: 1, 3, 9
Model answer
Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9.
Show that 91 is not a prime number.
Mark scheme
M1: finds a factor other than 1 and 91 (7 or 13); A1: 91 = 7 × 13 (so it has more than two factors)
Model answer
91 = 7 × 13, so 91 has factors other than 1 and 91. Therefore it is not prime.
Write down all the prime numbers between 30 and 50.
Mark scheme
M1: at least three correct and no composite numbers; A1: 31, 37, 41, 43, 47
Model answer
31, 37, 41, 43 and 47.
Bus A leaves a bus station every 12 minutes. Bus B leaves every 18 minutes. Both buses leave at 9:00 am. At what time will they next leave together?
Mark scheme
M1: lists multiples of 12 and 18 or uses LCM; A1: 36 minutes; A1: 9:36 am
Model answer
Multiples of 12: 12, 24, 36. Multiples of 18: 18, 36. The LCM is 36, so they next leave together at 9:36 am.
Explain why 2 is the only even prime number.
Mark scheme
B1: every other even number is divisible by 2; B1: so it has at least three factors (1, 2 and itself) / is not prime
Model answer
Every even number is a multiple of 2, so any even number bigger than 2 has at least three factors: 1, 2 and itself. Only 2 itself has just two factors.
Find a number between 20 and 30 that has exactly six factors. Show how you know.
Mark scheme
M1: lists factors of a number in the range; A1: 28; A1: factors 1, 2, 4, 7, 14, 28 (six factors)
Model answer
The factors of 28 are 1, 2, 4, 7, 14 and 28. That is exactly six factors. (The other numbers between 20 and 30 have different numbers of factors.)
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