Playing with Numbers quiz

Which of the following is a prime number?

The smallest prime number is:

The number of factors of 1 is:

A number is divisible by 9 if:

The HCF of 12 and 18 is:

The LCM of 4 and 6 is:

Which pair of numbers is co-prime?

The prime factorisation of 36 is:

Which number is divisible by 11?

The number of prime numbers between 1 and 20 is:

Write all the factors of 48. (2 marks)

Write the first five multiples of 13. (2 marks)

What are twin primes? Write two pairs of twin primes less than 20. (2 marks)

Express 36 as the sum of two odd primes in two different ways. (2 marks)

Is 5,445 divisible by 5 and by 9? Give reasons. (2 marks)

What is a perfect number? Show that 28 is a perfect number. (2 marks)

Find the common factors of 20 and 28. (2 marks)

Find the first three common multiples of 6 and 8. (2 marks)

Write the smallest 4-digit number and express it as a product of primes. (2 marks)

Why is every even number greater than 2 composite? (2 marks)

Find the HCF of 36, 60 and 84 using prime factorisation. (3 marks)

Find the LCM of 20, 25 and 30 using the division method. (3 marks)

Find the smallest number which when divided by 6, 15 and 18 leaves a remainder 5 in each case. (3 marks)

Find the greatest number of 4 digits which is divisible by 15, 25 and 40. (3 marks)

Find the HCF and LCM of 24 and 36, and verify that HCF x LCM = product of the two numbers. (3 marks)

Read the passage and answer the questions. Three traffic lights at a road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. They all change together at 7 a.m. (i) Is this an HCF or an LCM problem? Why? (ii) Find the time after which they will change together again. (iii) At what time will they next change together? (5 marks)

Read the passage and answer the questions. A school has 90 boys and 120 girls. For a cultural programme, the teacher wants to make groups such that each group has the same number of students and every group has only boys or only girls. (i) Find the greatest number of students in each group. (ii) How many groups of boys and of girls will be formed? (iii) Is this an HCF or LCM problem? Explain. (5 marks)

Read the passage and answer the questions. Ankit was testing the number 2,34,576 for divisibility. He found that the number formed by its last three digits is 576 and the sum of its digits is 27. (i) Is the number divisible by 8? Why? (ii) Is it divisible by 9? Why? (iii) Is it divisible by 72? Explain using co-prime factors. (5 marks)

Read the passage and answer the questions. A rectangular room is 825 cm long, 675 cm wide and 450 cm high. A carpenter wants a measuring rod that can measure all three dimensions an exact number of times. (i) What should be the longest such rod? (ii) How many times will the rod fit along the length? (iii) Name the concept used. (5 marks)

Read the passage and answer the questions. Priya visits the library every 4 days, Rohan every 6 days and Simran every 10 days. They all met at the library on 1 March. (i) After how many days will they meet again at the library? (ii) On what date will they next meet? (iii) How many times will Priya visit the library from 1 March up to and including the day they next meet? (5 marks)

State the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 and 11. Using the rules, test the number 15,840 for divisibility by each of 2, 3, 4, 5, 6, 8, 9, 10 and 11. (6 marks)

Draw factor trees for 120 and 150. Write the prime factorisation of each and use them to find the HCF and LCM of 120 and 150. Draw a Venn diagram showing the common prime factors. (6 marks)

Explain the Sieve of Eratosthenes with a diagram of numbers 1 to 50. List all primes and composites up to 50. Find the number of primes between 30 and 50, and explain why 2 is the only even prime. (6 marks)

Find the minimum length of a rope that can be cut into pieces of 25 cm, 30 cm or 45 cm with nothing left over. Then find the greatest length of a scale that can measure 2 m 25 cm, 3 m 60 cm and 4 m 5 cm exactly. Show prime factorisation for both. (6 marks)

Explain the difference between HCF and LCM with two real-life problems for each. Solve: (i) Find the HCF of 105, 175 and 245. (ii) Find the LCM of 8, 12 and 20. Show the working by the division method. (6 marks)