**Factor:** A number that divides another number exactly with no remainder. Example: 2, 3, 4, 6 are factors of 12.
**Multiple:** A number made by multiplying another number by a whole number. Example: 6, 9, 12, 15 are multiples of 3.
**Common Factor:** A number that divides two or more numbers exactly. Example: 2, 4 are common factors of 12 and 20.
**Common Multiple:** A number that is a multiple of two or more numbers. Example: 12, 24 are common multiples of 3 and 4.
**Prime Number:** A number with exactly 2 factors (1 and itself). Example: 13, 37, 5.
**Key Rules:** 1 is a factor of every number. Every number is a multiple of itself. To find common factors, list all factors and pick common ones. To find common multiples, use number lines or skip counting.
**Don't Confuse:** Factors are smaller (they divide the number), multiples are bigger (they contain the number).
Q1. Which of the following is a factor of 20?
Answer: A — 4 is a factor of 20 because 4 × 5 = 20, while 6, 7, and 9 do not divide 20 exactly.
Q2. Which number is a multiple of 5?
Answer: B — 25 is a multiple of 5 because 5 × 5 = 25, while the others cannot be made by multiplying 5 by a whole number.
Q3. What are the common factors of 12 and 18?
Answer: A — Factors of 12 are 1, 2, 3, 4, 6, 12 and factors of 18 are 1, 2, 3, 6, 9, 18; the common ones are 1, 2, 3, 6.
Q4. Which of the following is NOT a factor of 24?
Answer: B — 5 does not divide 24 exactly because 24 ÷ 5 = 4.8 with a remainder, while 3, 6, and 8 all divide 24 exactly.
Q5. Which number is a common multiple of 4 and 6?
Answer: C — 24 is a common multiple because 4 × 6 = 24 and 6 × 4 = 24, while 18 is only a multiple of 6, 20 is only a multiple of 4, and 26 is neither.
Q6. What are the common factors of 15 and 25? (Fill in the blanks: _____ and _____)
Answer: B — Factors of 15 are 1, 3, 5, 15 and factors of 25 are 1, 5, 25; the common factors are 1 and 5.
Q7. Mowgli jumps by 3 steps starting from 0. Which number will he touch?
Answer: B — Jumping by 3 steps from 0 touches 3, 6, 9, 12, 15, 18... so Mowgli lands on 18, which is a multiple of 3.
Q8. Which of the following numbers is a prime number?
Answer: C — 13 is a prime number because it has only 2 factors (1 and 13), while 15, 21, and 12 have more than 2 factors.
Q9. A rabbit jumps by 4 and a deer jumps by 6. On which number do they both first land together?
Answer: B — The rabbit touches 4, 8, 12, 16... and the deer touches 6, 12, 18... so they first meet at 12, which is the least common multiple.
Q10. In an array of 2 rows with 7 dots in each row, the factors shown are _____ and _____.
Answer: C — An array of 2 rows with 7 dots in each row shows 2 × 7 = 14, so the factors shown are 2 and 7.
What is a factor of a number?
A factor is a number that divides another number completely with no remainder — for example, 3 is a factor of 12 because 3 × 4 = 12.
What is a multiple of a number?
A multiple is a number we get when we multiply a number by another whole number — for example, 15 is a multiple of 3 because 3 × 5 = 15.
What are common factors?
Common factors are numbers that divide two or more numbers exactly — for example, 2 and 4 are common factors of 12 and 20.
What are common multiples?
Common multiples are numbers that are multiples of two or more numbers — for example, 12 is a common multiple of 3 and 4 because both 3 and 4 divide it exactly.
What is a prime number?
A prime number has only two factors: 1 and itself — for example, 13 is prime because only 1 and 13 divide it exactly.
Is 1 a factor of every number?
Yes, 1 is always a factor of every number because any number divided by 1 equals itself.
Is every number a multiple of itself?
Yes, every number is a multiple of itself because the number multiplied by 1 equals itself.
How do you find factors of a number using arrays?
Make rectangular arrangements of dots or objects: if you can arrange a number into equal rows and columns, the row and column sizes are its factors — for example, 12 can be arranged as 3 × 4, so 3 and 4 are factors.
How do you find common factors of two numbers?
List all factors of both numbers, then pick the ones that appear in both lists — for example, factors of 12 are 1, 2, 3, 4, 6, 12 and factors of 18 are 1, 2, 3, 6, 9, 18, so common factors are 1, 2, 3, 6.
How do you find common multiples using a number line?
Mark jumps for both numbers on a number line and see where they land on the same spots — for example, jumping by 3 and jumping by 4 both touch 12, so 12 is a common multiple.
What is a factor? Give one example. [1 mark]
A factor divides a number exactly. Use the definition: if a × b = number, then a and b are factors.
Write all the factors of 16. How many factors does 16 have? [2 marks]
Find all numbers that divide 16 exactly: 1 × 16, 2 × 8, 4 × 4. Count them all.
A rabbit jumps by 2 steps and a frog jumps by 3 steps from 0. On a number line, which are the first three common multiples they will touch? Explain how you found them. [3 marks]
Mark jumps for 2: 2, 4, 6, 8, 10, 12... and jumps for 3: 3, 6, 9, 12, 15, 18... Find where they both land (common multiples).
Find all common factors of 24 and 36. Show how each factor divides both numbers exactly. What is the largest common factor? [5 marks]
List all factors of 24 (1, 2, 3, 4, 6, 8, 12, 24) and all factors of 36 (1, 2, 3, 4, 6, 9, 12, 18, 36). Write division checks like 24 ÷ 2 = 12 and 36 ÷ 2 = 18. Pick common ones and find the largest.
True or False: A number can have more factors than multiples. Give a reason for your answer. [2 marks]
Think about 12: its factors are 1, 2, 3, 4, 6, 12 (only 6 factors), but its multiples are 12, 24, 36, 48... (endless multiples).
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