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Playing with Numbers — Chapter Test

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Q1
Which is the odd one out (three are prime numbers)?
4 = 2 × 2 is composite; the others are prime.
Q2
Which number is divisible by 11?
253 ÷ 11 = 23, so it is divisible by 11.
Q3
The HCF of two numbers is their ___ common factor.
HCF is the highest common factor.
Q4
Which of these is a composite number?
15 = 3 × 5 is composite.
Q5
What is the prime factorisation of 36?
36 = 2 × 2 × 3 × 3.
Q6
What is the HCF of 24 and 36?
The highest common factor of 24 and 36 is 12.
Q7
What is the LCM of 6 and 9?
The smallest common multiple of 6 and 9 is 18.
Q8
Is 456 divisible by 8?
456 ÷ 8 = 57, so yes.
Q9
Is 4,521 divisible by 3?
Digit sum 4 + 5 + 2 + 1 = 12, divisible by 3, so yes.
Q10
How many factors does 12 have?
Factors of 12 are 1, 2, 3, 4, 6, 12 — that is 6.
Q11
Two ropes of 18 m and 24 m are cut into equal pieces of the greatest length. What is that length?
Greatest length = HCF of 18 and 24 = 6 m.
Q12
Two bells ring every 8 and 12 minutes. After how many minutes do they ring together?
They ring together at the LCM of 8 and 12, which is 24 minutes.
Q13
What is the smallest number divisible by 2, 3, 4, 5 and 6?
The LCM of 2, 3, 4, 5 and 6 is 60.
Q14
The HCF of 12 and 18 is 6 and the LCM is 36. What is HCF × LCM?
6 × 36 = 216, which also equals 12 × 18.
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