Revision Library

revisionlibrary.co.uk

FOUNDATION

1.11D Factors and Multiples: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down all the factors of 24.

(Total for Question 1 is 1 mark)

Write down the first five multiples of 7 that are less than 40.

(Total for Question 2 is 1 mark)

Is 29 a prime number? State your answer.

(Total for Question 3 is 1 mark)

Work out the highest common factor (HCF) of 42 and 56.

(Total for Question 4 is 2 marks)

Work out the least common multiple (LCM) of 6 and 15.

(Total for Question 5 is 2 marks)

Write 180 as a product of prime factors.

(Total for Question 6 is 2 marks)

Work out the smallest positive integer that is a multiple of 4, 6 and 9.

(Total for Question 7 is 2 marks)

Sam and Aisha practise the same music piece in cycles. Sam repeats it every 8 days, Aisha every 12 days. If they both practise today, after how many days will they next practise together?

(Total for Question 8 is 2 marks)

List all factors of 90 that are also multiples of 3.

(Total for Question 9 is 2 marks)

Decide whether 51 is prime or composite. Give a short reason.

(Total for Question 10 is 1 mark)

Priya has two ribbons of lengths 24 m and 40 m. She wants to cut both ribbons into identical shorter pieces with integer lengths and no waste. Work out the greatest possible length of each piece in metres.

(Total for Question 11 is 2 marks)

Work out the least common multiple of 14, 21 and 35.

(Total for Question 12 is 2 marks)

How many prime numbers are there between 1 and 50 inclusive?

(Total for Question 13 is 1 mark)

Show that 123456 is divisible by 3.

(Total for Question 14 is 2 marks)

Two positive integers have HCF 6 and LCM 84. Work out the product of the two integers.

(Total for Question 15 is 2 marks)

Work out the smallest 3-digit integer that is divisible by both 11 and 13.

(Total for Question 16 is 1 mark)

The Year 7 class has football training every 5 days and the Year 8 class every 7 days. If both classes have training on Monday, after how many days will they next have training on the same day?

(Total for Question 17 is 2 marks)

How many positive integers less than 100 are divisible by at least one of 2, 3 or 5? Show your working.

(Total for Question 18 is 3 marks)

Mark scheme · 1.11D Factors and Multiples: Fluency and Exam Drill

Question 1

B1 All factors listed: 1, 2, 3, 4, 6, 8, 12, 24 cao
Answer: 1, 2, 3, 4, 6, 8, 12, 24 (any order accepted)

Question 2

B1 Multiples: 7, 14, 21, 28, 35 cao
Answer: 7, 14, 21, 28, 35

Question 3

B1 29 is prime cao
Answer: 29 is prime.

Question 4

M1 Correct method: list common factors or prime factorisation (e.g. 42 = 2*3*7, 56 = 2³*7) or explicit common factors
A1 14 cao
Answer: 14

Question 5

M1 Correct method: prime factors or listing multiples (6 = 2*3, 15 = 3*5 so LCM = 2*3*5)
A1 30 cao
Answer: 30

Question 6

M1 Correct factor tree or prime factor method shown (e.g. 180 ÷ 2 = 90, etc.)
A1 180 = 2² * 3² * 5 cao
Answer: 2² * 3² * 5

Question 7

M1 Correct method: prime factors or pairwise LCMs (4 = 2², 6 = 2*3, 9 = 3² so LCM = 2² * 3²)
A1 36 cao
Answer: 36

Question 8

M1 Find LCM of 8 and 12 (method shown)
A1 24 days cao
Answer: 24 days

Question 9

M1 Correct method: list factors of 90 or note factors that are divisible by 3
A1 3, 6, 9, 15, 18, 30, 45, 90 cao
Answer: 3, 6, 9, 15, 18, 30, 45, 90 (any order)

Question 10

B1 51 is composite, e.g. 51 = 3 * 17 cao
Answer: Composite, because 51 = 3 * 17.

Question 11

M1 Correct method to find HCF of 24 and 40 (e.g. prime factors or Euclid's algorithm)
A1 8 metres cao
Answer: 8 m

Question 12

M1 Correct method: prime factors (14 = 2*7, 21 = 3*7, 35 = 5*7) and combine
A1 210 cao
Answer: 210

Question 13

B1 15 cao
Answer: 15

Question 14

M1 Use digit sum method: 1+2+3+4+5+6 = 21
A1 Therefore 123456 is divisible by 3 cso
Answer: Digits sum to 21 and 21 is divisible by 3, so 123456 is divisible by 3.

Question 15

M1 Use property: product = HCF * LCM for two integers
A1 504 cao
Answer: 504

Question 16

B1 143 cao
Answer: 143

Question 17

M1 Find LCM of 5 and 7 (method shown)
A1 35 days cao
Answer: 35 days

Question 18

M1 Count multiples: floor(99/2)=49, floor(99/3)=33, floor(99/5)=19
M1 Subtract pairwise intersections floor(99/6)=16, floor(99/10)=9, floor(99/15)=6
A1 Apply inclusion-exclusion: 49+33+19 -16-9-6 +3 = 73 cao
Answer: 73

Factors and Multiples: Fluency and Exam Drill - Worksheets, Questions and Revision