Here is a list of numbers. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
(a)From the list, write down all the prime numbers.(2)
(b)From the list, write down all the square numbers.(1)
(Total for Question 3 is 3 marks)
4
Which of these numbers is a multiple of 9?
A) 42
B) 54
C) 65
D) 80
(Total for Question 4 is 1 mark)
5
Here is a list of numbers. 6, 8, 12, 15, 24, 30 Circle the two numbers in the list that are common multiples of 3 and 4.
(Total for Question 5 is 2 marks)
6
State whether each statement is True or False.
(a)3 is a factor of 27.(1)
(b)5 is a multiple of 20.(1)
(c)1 is a factor of every whole number.(1)
(d)9 is a prime number.(1)
(Total for Question 6 is 4 marks)
7
Which of these numbers is NOT a factor of 40?
A) 5
B) 8
C) 9
D) 10
(Total for Question 7 is 1 mark)
8
Complete the table below. Each row is missing one number.
(Total for Question 8 is 4 marks)
9
Find the Highest Common Factor (HCF) of 12 and 18.
(Total for Question 9 is 2 marks)
10
Find the Lowest Common Multiple (LCM) of 4 and 6.
(Total for Question 10 is 2 marks)
11
Priya is making identical party bags. She has 16 chocolate bars and 24 packets of crisps. Every bag must contain the same number of chocolate bars and the same number of packets of crisps, with none left over. Work out the greatest number of party bags Priya can make.
(Total for Question 11 is 3 marks)
12
Two lighthouses flash together at 8:00 pm. Lighthouse A then flashes every 15 seconds. Lighthouse B then flashes every 20 seconds. Work out how many seconds after 8:00 pm the two lighthouses will next flash together.
(Total for Question 12 is 3 marks)
13
Find the Highest Common Factor (HCF) of 30, 45 and 60.
(Total for Question 13 is 3 marks)
14
Find the Lowest Common Multiple (LCM) of 5, 6 and 9.
(Total for Question 14 is 3 marks)
15
Explain why 2 is the only even prime number.
(Total for Question 15 is 2 marks)
16
Sam says, "If a number is a multiple of 6, it must also be a multiple of 3." Is Sam correct? Give a reason for your answer.
(Total for Question 16 is 2 marks)
17
Three bells ring together at 12:00 noon. Bell A rings every 6 minutes. Bell B rings every 8 minutes. Bell C rings every 10 minutes. Work out the next time after 12:00 noon that all three bells ring together.
(Total for Question 17 is 3 marks)
Mark scheme · 1.11 Factors and Multiples
Question 1
B1 7, 14, 21, 28, 35 all correct
Answer: 7, 14, 21, 28, 35
Question 2
B1 at least 4 correct factors identified
B1 fully correct set 1, 2, 4, 5, 10, 20 with no extra numbers, oe order
Answer: 1, 2, 4, 5, 10, 20
Question 3
(a) B1 at least 3 correct primes with no more than 1 non-prime included
(a) B1 fully correct set 2, 3, 5, 7, 11 cao
(a) Answer: 2, 3, 5, 7, 11
(b) B1 4 and 9 cao, both values with no extras
(b) Answer: 4, 9
Question 4
B1 B (54) cao
Answer: B) 54
Question 5
B1 12 identified
B1 24 identified, with no incorrect extra numbers circled
Answer: 12 and 24
Question 6
(a) B1 True cao, since 27 = 3 x 9
(a) Answer: True
(b) B1 False cao, since 5 does not appear in the 20 times table
(b) Answer: False
(c) B1 True cao
(c) Answer: True
(d) B1 False cao, since 9 = 3 x 3 has a factor other than 1 and itself
(d) Answer: False
Question 7
B1 C (9) cao
Answer: C) 9
Question 8
B1 27 cao (third multiple of 9)
B1 4 cao (missing factor of 16)
B1 33 cao (third multiple of 11)
B1 4 cao (missing factor of 24)
Answer: 27, 4, 33, 4
Question 9
M1 correct list of factors of 12 (1,2,3,4,6,12) and 18 (1,2,3,6,9,18), or other correct method
A1 6 cao
Answer: 6
Question 10
M1 correct list of multiples of 4 (4,8,12,16,...) and 6 (6,12,18,...), or other correct method
A1 12 cao
Answer: 12
Question 11
M1 identifying that the HCF of 16 and 24 is required
M1 correct factors of 16 (1,2,4,8,16) and 24 (1,2,3,4,6,8,12,24) or other valid method
A1 8 cao
Answer: 8 party bags
Question 12
M1 identifying that the LCM of 15 and 20 is required
M1 correct multiples of 15 (15,30,45,60) and 20 (20,40,60) or other valid method
A1 60 seconds cao (accept 1 minute)
Answer: 60 seconds
Question 13
M1 correct factors of at least two of the three numbers
M1 correct factors of all three numbers: 30 (1,2,3,5,6,10,15,30), 45 (1,3,5,9,15,45), 60 (1,2,3,4,5,6,10,12,15,20,30,60)
A1 15 cao
Answer: 15
Question 14
M1 correct multiples of at least two of the three numbers
M1 correct multiples of all three numbers leading to a common value, e.g. multiples of 5 up to 90, multiples of 6 up to 90, multiples of 9 up to 90
A1 90 cao
Answer: 90
Question 15
B1 recognising that every even number greater than 2 has 2 as a factor as well as 1 and itself, so it has more than two factors
B1 concluding that 2 itself only has the factors 1 and 2, so 2 is prime, oe
Answer: Every even number greater than 2 can be divided exactly by 2, so it has at least three factors (1, 2 and itself), meaning it cannot be prime. 2 itself has only the factors 1 and 2, so 2 is prime and is the only even prime number.
Question 16
B1 Yes, Sam is correct
B1 valid reason, e.g. 6 = 2 x 3, so any multiple of 6 is 6 x k = 3 x (2k), which is a multiple of 3, oe
Answer: Yes, Sam is correct
Question 17
M1 identifying that the LCM of 6, 8 and 10 is required
M1 correct method leading to LCM=120, e.g. multiples of 6, 8 and 10 up to 120, or prime factors 6=2x3, 8=23, 10=2x5 giving 23x3x5=120
A1 2:00 pm cao (ft their correct 120 minutes converted to a time)