Here is a list of numbers. 14, 18, 21, 25, 28, 33, 36, 40 Write down all the multiples of 7 from the list.
(Total for Question 1 is 2 marks)
2
Write down all the factor pairs of 32.
(Total for Question 2 is 2 marks)
3
Here is a list of numbers. 1, 2, 4, 6, 8, 9, 11, 13, 16, 27
(a)From the list, write down all the prime numbers.(2)
(b)From the list, write down all the cube numbers.(1)
(Total for Question 3 is 3 marks)
4
Which of these numbers is a factor of 45?
A) 6
B) 9
C) 14
D) 20
(Total for Question 4 is 1 mark)
5
A list of numbers is shown below. 9, 15, 20, 30, 33, 40 Circle the two numbers that are common multiples of 3 and 5.
(Total for Question 5 is 2 marks)
6
State whether each statement about the number 84 is True or False.
(a)84 is a multiple of 9.(1)
(b)84 is a factor of 168.(1)
(c)84 is a prime number.(1)
(d)The Highest Common Factor of 84 and 36 is 12.(1)
(Total for Question 6 is 4 marks)
7
28 and 42 are two numbers. Find their Highest Common Factor (HCF).
(Total for Question 7 is 2 marks)
8
9 and 12 are two numbers. Find their Lowest Common Multiple (LCM).
(Total for Question 8 is 2 marks)
9
Here is a factor tree for 60. Complete the missing part of the tree, then write 60 as a product of its prime factors.
Figure (to be drawn): A factor tree diagram. At the top is the number 60, with two branches leading down to 6 and 10. The branch from 6 splits into 2 and 3, both circled to show they are prime. The branch from 10 splits into 2 (already shown, circled) and a blank box, which the student must fill in.
(Total for Question 9 is 2 marks)
10
Show that 8 is a common factor of 56 and 72.
(Total for Question 10 is 2 marks)
11
Chidi is finding the Highest Common Factor of 16 and 40. His working is shown below. Factors of 16: 1, 2, 4, 8, 16 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 Common factors: 1, 2, 4, 8 Chidi writes: 'The Highest Common Factor of 16 and 40 is 4.' Explain the mistake Chidi has made, and write down the correct Highest Common Factor.
(Total for Question 11 is 2 marks)
12
A whole number has these three properties: - it is a multiple of 6 - it is a factor of 90 - it is greater than 20 and less than 50 Find the number.
(Total for Question 12 is 3 marks)
13
Neha runs a flower stall and has 42 tulips and 63 daffodils to arrange. She wants to make identical bunches, using every flower, with none left over. Work out the greatest number of identical bunches she can make.
(Total for Question 13 is 3 marks)
14
Anil waters his tomato plants every 18 days and waters his rose bushes every 24 days. He waters both on the same day today. Work out in how many days' time he will next water both the tomato plants and the rose bushes on the same day.
(Total for Question 14 is 3 marks)
15
Zara says, 'If a number is a factor of 20, it must also be a factor of 30.' Is Zara correct? Give a reason for your answer.
(Total for Question 15 is 2 marks)
16
Explain why every multiple of 10 is also a multiple of 5.
(Total for Question 16 is 2 marks)
17
Amara, Tomasz and Ffion go jogging together and set off at the same time from the start of a park route. Amara completes a lap every 8 minutes. Tomasz completes a lap every 12 minutes. Ffion completes a lap every 20 minutes. Work out how many minutes after setting off all three will next be at the start together.
(Total for Question 17 is 3 marks)
Mark scheme · 1.11B Factors and Multiples (Part 2)
Question 1
B1 at least two correct multiples identified, with no more than one non-multiple included
B1 fully correct set 14, 21, 28 cao
Answer: 14, 21, 28
Question 2
B1 at least 2 correct factor pairs identified
B1 fully correct set (1,32), (2,16), (4,8) with no extra pairs, oe order
Answer: (1, 32), (2, 16), (4, 8)
Question 3
(a) B1 at least 2 correct primes with no more than 1 non-prime included
(a) B1 fully correct set 2, 11, 13 cao
(a) Answer: 2, 11, 13
(b) B1 1, 8 and 27 cao, all three values with no extras
(b) Answer: 1, 8, 27
Question 4
B1 B (9) cao
Answer: B) 9
Question 5
B1 15 identified
B1 30 identified, with no incorrect extra numbers circled
Answer: 15 and 30
Question 6
(a) B1 False cao, since 84/9 = 9.33... is not a whole number
(a) Answer: False
(b) B1 True cao, since 168 = 84 x 2
(b) Answer: True
(c) B1 False cao, since 84 = 2 x 2 x 3 x 7 has factors other than 1 and itself
(c) Answer: False
(d) B1 True cao
(d) Answer: True
Question 7
M1 correct list of factors of 28 (1,2,4,7,14,28) and 42 (1,2,3,6,7,14,21,42), or other correct method
A1 14 cao
Answer: 14
Question 8
M1 correct list of multiples of 9 (9,18,27,36,...) and 12 (12,24,36,...), or other correct method
A1 36 cao
Answer: 36
Question 9
M1 the missing branch correctly completed as 5
A1 60 = 2 x 2 x 3 x 5 (or 22 x 3 x 5) oe, cao
Answer: Missing branch = 5; 60 = 2 x 2 x 3 x 5 (or 22 x 3 x 5)
Question 10
B1 56 / 8 = 7 (or 8 x 7 = 56) shown
B1 72 / 8 = 9 (or 8 x 9 = 72) shown, cso
Answer: 8 is a common factor of 56 and 72 (56 = 8x7, 72 = 8x9)
Question 11
B1 identifies that Chidi has not chosen the highest number from his own list of common factors (he wrote 4 instead of 8), oe
B1 8 cao
Answer: Chidi's factors and common factors (1, 2, 4, 8) are correct, but he has not picked the highest of these - the Highest Common Factor is 8, not 4.