Write down two factors of 36 that are greater than 6.
(1)
2
Is 29 a prime number? Explain your answer in one sentence.
(1)
3
Complete the sequence with the next two multiples of 7: 7, 14, 21, 28, ...
(1)
4
Circle the two square numbers from this list: 20, 25, 30, 36.
(1)
5
List all the factors of 30.
(2)
6
What is the smallest prime number greater than 50?
(1)
7
Hannah says 91 is prime. Is she correct? Explain your answer.
(2)
8
Find the highest common factor (HCF) of 24 and 36. Show a method.
(2)
9
Write down two consecutive square numbers greater than 9. Give both numbers.
(1)
10
Amir multiplies a number by 9 and gets 81. What was his original number? Show your working.
(2)
11
Which number between 40 and 60 has exactly three factors? Write the number and list its factors.
(2)
12
Sara writes down every multiple of 8 up to and including 80. How many numbers does she write? Show your working.
(3)
13
Is 1 a prime number? Tick yes or no and give a short reason.
Yes
No
14
Work out the least common multiple (LCM) of 12 and 15. Show prime factors or list multiples to support your answer.
(3)
15
Find all the prime numbers between 20 and 40. Show how you checked them if you need to.
(3)
16
Is 121 a prime number? Explain your answer.
(2)
17
Find two square numbers that are less than or equal to 100 and add to 181. Explain how you know you have found them.
(2)
18
A teacher asks pupils to write every whole number from 1 to 48 inclusive. Circle the numbers that are multiples of both 3 and 4. How many numbers should be circled? Show how you worked this out.
(3)
Mark scheme · KS2.M-Y5N4 Factors, Multiples, Primes and Squares
Question 1
B1 Any two correct factors greater than 6, for example 9 and 12 cao
Answer: 9, 12
Question 2
B1 Correct explanation that 29 has no divisors other than 1 and itself, or states it is prime cao
Answer: Yes. 29 is prime because it has no factors other than 1 and 29.
Question 3
B1 Next two multiples 35 and 42 cao
Answer: 35, 42
Question 4
B1 25 and 36 circled cao
Answer: 25, 36
Question 5
B1 Most correct factors given (follow through allowed) oe
B1 All factors 1, 2, 3, 5, 6, 10, 15, 30 cao
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Question 6
B1 53 cao
Answer: 53
Question 7
B1 Identify that 91 is divisible by 7 (or 13) or show 91 = 7 x 13
B1 Conclude that 91 is not prime cao
Answer: No. 91 = 7 x 13 so it is not prime.
Question 8
M1 Correct method shown, e.g. listing common factors or prime factor method
B1 HCF = 12 cao
Answer: 12
Question 9
B1 Any two consecutive squares greater than 9, for example 16 and 25 cao
Answer: 16, 25
Question 10
M1 Correct operation to undo multiplication, e.g. 81 ÷ 9 seen
B1 Original number 9 cao
Answer: 9
Question 11
B1 Identify number 49 (a square of a prime) or equivalent
B1 List factors 1, 7, 49 cao
Answer: 49; 1, 7, 49
Question 12
M1 Method shown to count multiples, e.g. 80 ÷ 8 or listing multiples
B1 Correct count 10 cao
B1 Supporting statement or listing of multiples 8, 16, ..., 80 oe
Answer: 10
Question 13
B1 No and reason that 1 has only one factor so it is not prime cao
Answer: No. 1 is not prime because it has only one factor (1) not two.
Question 14
M1 Method shown using prime factors or listing multiples
B1 LCM = 60 cao
B1 Supporting evidence such as 12 x 5 = 60 or 15 x 4 = 60 oe
Answer: 60
Question 15
M1 Method shown to check divisibility or explain elimination of composites
B2 All primes correctly listed: 23, 29, 31, 37 cao
Answer: 23, 29, 31, 37
Question 16
B1 Show that 121 = 11 x 11 or state a factorisation
B1 Conclude that 121 is not prime cao
Answer: No. 121 = 11 x 11 so it is not prime.
Question 17
M1 Method shown, e.g. list squares up to 100 or test pairs
B1 Correct pair 81 and 100 given and sum shown to be 181 cao
Answer: 81, 100
Question 18
M1 Method shown to find numbers that are multiples of both 3 and 4, e.g. recognise LCM = 12 or show listing