**Multiples:** Numbers created by skip-counting. Multiples of 3 are 3, 6, 9, 12, 15... Multiples grow larger.
**Factors (or Divisors):** Numbers that divide evenly. Factors of 12 are 1, 2, 3, 4, 6, 12. Factors are smaller.
**Common Multiples:** Appear in both lists (e.g. 15, 30, 45 are common multiples of 3 and 5).
**Common Factors:** Divide both numbers (e.g. 1, 2 are common factors of 14 and 36).
**Prime Numbers:** Exactly 2 factors (1 and itself) → 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
**Composite Numbers:** More than 2 factors → 4, 6, 8, 9, 10, 12, 14, 15...
**Key Facts:** Number 1 is neither prime nor composite. 2 is the only even prime. Every number's smallest factor is 1, and largest factor is itself.
**Diagrams to Remember:** Idli-Vada Venn diagram showing overlapping circles of multiples of 3 and 5; rectangular arrangements of numbers showing factors.
**Don't Confuse:** Multiples keep growing (5, 10, 15...) but factors stay same size or smaller (20 has factors 1, 2, 4, 5, 10, 20). Prime means FEW factors (exactly 2), composite means MANY factors (more than 2).
Q1. Which of these is a multiple of 5?
Answer: B — 35 = 5 × 7, so it is a multiple of 5; the others when divided by 5 leave a remainder.
Q2. What are all the factors of 12?
Answer: A — All numbers that divide 12 exactly with no remainder are 1, 2, 3, 4, 6, and 12.
Q3. Which number is prime?
Answer: C — 17 has exactly 2 factors (1 and 17); 1 has only one factor, 15 and 20 have many factors.
Q4. In the idli-vada game up to 30, how many times do you say 'idli-vada'?
Answer: B — Common multiples of 3 and 5 up to 30 are 15 and 30, so 'idli-vada' is said 2 times.
Q5. What is the smallest common multiple of 4 and 6?
Answer: C — 12 is the first number that appears in both multiples of 4 (4, 8, 12...) and multiples of 6 (6, 12...).
Q6. Which of the following is a composite number?
Answer: C — 18 has factors 1, 2, 3, 6, 9, 18 (more than 2 factors); 2, 13, 19 are all prime numbers.
Q7. In Jump Jackpot, which jump size will reach both 20 and 30?
Answer: B — 10 is a common factor of 20 (20 = 10 × 2) and 30 (30 = 10 × 3); other options don't divide both numbers.
Q8. Which statement is TRUE?
Answer: C — 2 is prime with factors 1 and 2; it is the only even prime because all other even numbers have 2 as a factor.
Q9. __________ are numbers that have exactly two factors: 1 and the number itself.
Answer: B — By definition, prime numbers have exactly 2 factors; composite numbers have more than 2 factors.
Q10. Look at the Venn diagram of multiples of 3 and 5 up to 30. Which number appears in the overlapping region?
Answer: C — 15 is a multiple of both 3 and 5 (15 = 3 × 5), so it is in the common region; others are multiples of only one.
What are multiples of 3?
Numbers you get by skip-counting by 3: 3, 6, 9, 12, 15, 18, and so on.
What is a factor of 24?
A factor is any number that divides 24 exactly with no remainder: 1, 2, 3, 4, 6, 8, 12, and 24.
What are common multiples?
Numbers that appear in the multiple list of two or more numbers, like 15, 30, 45 for both 3 and 5.
What are common factors?
Numbers that divide two or more numbers exactly, like 1 and 2 are common factors of 14 and 36.
Define a prime number.
A number with exactly 2 factors: 1 and itself, like 2, 3, 5, 7, 11, 13, 17, 19.
Define a composite number.
A number with more than 2 factors, like 4, 6, 8, 9, 10, 12 that can be arranged in different rectangular ways.
Why is 1 not prime or composite?
The number 1 has only one factor (itself), but prime and composite numbers must have at least 2 or more than 2 factors.
In the idli-vada game, when do you say 'idli-vada'?
Say 'idli-vada' for numbers that are multiples of BOTH 3 and 5, like 15, 30, 45, 60.
What jump sizes will land on 36 in Jump Jackpot?
Any factor of 36 works as a jump size: 1, 2, 3, 4, 6, 9, 12, 18, or 36.
Which is the smallest common multiple of 3 and 5?
The smallest common multiple of 3 and 5 is 15 (which equals 3 × 5).
What is a multiple? Give one example. [1 mark]
A multiple is a number made by skip-counting by that number. For example, multiples of 4 are 4, 8, 12, 16...
Find all common factors of 12 and 18. [2 marks]
List all factors of 12 (1, 2, 3, 4, 6, 12) and all factors of 18 (1, 2, 3, 6, 9, 18). Then circle the numbers that appear in BOTH lists.
In the idli-vada game, explain with an example when a player should say 'idli-vada' instead of a number. Why do we call these numbers common multiples? [3 marks]
A player says 'idli-vada' when the number is a multiple of BOTH 3 and 5 (like 15). These are called common multiples because 15 is in BOTH the list of multiples of 3 AND the list of multiples of 5.
Guna wants to arrange 12 mangoes and Anshu wants to arrange 7 mangoes in rectangular rows and columns. (a) In how many ways can Guna arrange 12 mangoes? (b) In how many ways can Anshu arrange 7 mangoes? (c) Explain why Guna has more arrangements than Anshu using the words 'factors' or 'prime number' or 'composite number.' [5 marks]
For Guna: find all factors of 12 (1×12, 2×6, 3×4) = 3 ways. For Anshu: find all factors of 7 (1×7 only) = 1 way. Explain: 12 is composite (has many factors), so many rectangle arrangements. 7 is prime (has only 2 factors: 1 and 7), so only 1 rectangle arrangement.
True or False: (a) The number 2 is a prime number. (b) Every composite number can be arranged in more than one rectangular way. Give a reason for each. [2 marks]
(a) True: 2 has exactly 2 factors (1 and 2). (b) True: Composite numbers have more than 2 factors, so they can form different rectangle arrangements like 12 = 2×6, 3×4, 1×12.
Practice with interactive flashcards, mind maps, upload your own chapters and get AI study kits instantly
Try StudyOS Free →