Practice Questions
Prime Time
What is the only even prime number?
Explain the difference between a prime number and a composite number. Provide one example for each.
List all the factors of 18.
Justify why 2 is the only even prime number.
Propose a number whose prime factorization consists of three identical prime numbers, where the prime number itself is the smallest two-digit prime number.
Calculate the prime factorization of 180.
Analyze if the numbers 27 and 35 are co-prime.
Define a prime number.
Evaluate the statement: "The sum of any two consecutive prime numbers is always an even number." Justify whether this statement is always true, sometimes true, or never true.
Identify which of the following is a composite number: .
Evaluate the statement: 'If a number is divisible by 8, it must also be divisible by 4.' Justify your reasoning using prime factorization.
Three bells ring at intervals of 6, 8, and 12 minutes respectively. If they ring together at 3:00 PM, at what time will they ring together next?
List all the prime numbers that are between 20 and 40.
Describe the divisibility rules for 2, 5, and 10. Use these rules to determine if the number 7850 is divisible by each of these numbers, explaining your reasoning.
Calculate the first three common multiples of 4 and 6.
Solve the following riddle: I am a number between 50 and 60. I am a multiple of 3. When I am divided by 5, I leave a remainder of 1. What number am I?
Calculate the smallest 4-digit number that is exactly divisible by 15.
Examine the numbers from 40 to 50 and list all the prime numbers.
Calculate the LCM of 15, 20, and 30 using the prime factorization method.
Propose a method to find the smallest 3-digit number which is a common multiple of 4 and 6. Justify your method using the concept of Least Common Multiple (LCM).
A student claims that to check if a number is divisible by 12, you only need to check if it is divisible by 2 and 6. Critique this statement and justify your reasoning with a counterexample.
Explain the divisibility rule for 4. Using this rule, identify if the number 3148 is divisible by 4.
Explain the concept of prime factorisation. Then, find the prime factorisation of the number 120 by drawing a factor tree.
Define what common factors are. Then, list all the factors for the numbers 24 and 36, and identify all their common factors.
Define co-prime numbers.
List the first five multiples of 6 and the first five multiples of 9. Then, identify their first common multiple.
Recall the Sieve of Eratosthenes method. Describe the first three steps to find prime numbers up to 50.
Apply the divisibility test to determine if 78536 is divisible by 8.
Calculate the HCF of 48, 72, and 108 using the prime factorization method.
Formulate a general statement about the prime factorization of a perfect square number. Justify your formulation with at least two examples.
Using prime factorization, examine if 36 is a factor of 1296. Do not perform long division.
Justify why the divisibility test for 4 works by examining the number 136. Your justification should explain why only the last two digits are relevant.
Evaluate: 'If a number is co-prime with 10, its last digit must be 1, 3, 7, or 9.' Justify your conclusion.
Create a pair of two-digit composite numbers that are co-prime. Justify your answer using prime factorization.
Justify why any two consecutive whole numbers (e.g., 8 and 9) are always co-prime.
Propose what the two numbers in an 'idli-vada' game could be if 'idli-vada' is first said at 42. Justify your answer.
Summarize the properties of the number 1 in the context of prime and composite numbers. Then, explain why the number 6 is called a 'perfect number' by listing its factors and checking the condition.
Calculate the greatest number that will divide 148, 246, and 623 leaving remainders 4, 6, and 11 respectively.
Anshu, Guna, and Radha are playing a game. Anshu says 'Tick' on every multiple of 3. Guna says 'Tock' on every multiple of 4. Radha says 'Clock' on every multiple of 5. They count from 1 to 200. Analyze and calculate: a) How many times will they say 'Tick-Tock-Clock' together? b) How many times will only 'Tick-Tock' be said (without 'Clock')?
Create a 4-digit number that is divisible by 8 and 5, but not by 3. Justify that your created number meets all these conditions.
Identify which of the following pairs of numbers are co-prime. Explain your reasoning. a) 8 and 15 b) 12 and 21 c) 7 and 49
In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm, and 90 cm respectively. Calculate the minimum distance each should walk so that all can cover the same distance in complete steps. Also, analyze how many steps each person will take to cover that distance.
Design a new game called 'Prime-Factor'. In this game, two players choose a number between 50 and 100. The player whose number has more distinct prime factors wins. Create a scenario where Player A chooses 60. Propose a winning number for Player B and justify why it wins.
Critique the following statement: 'A prime number is a number that is only divisible by 1 and itself.' Why is this definition incomplete? Propose a more precise definition.
A rectangular courtyard is 18 meters 72 cm long and 13 meters 20 cm wide. It is to be paved with square tiles of the same size. Calculate the largest possible size of such a tile.