Animal Jumps
Factors, multiples, common factors, common multiples, and prime numbers, explained with jumps on a number line.
- What factors and multiples are
- Finding factors using arrays (rows and columns)
- Prime numbers: numbers with only two factors
- Common multiples: where two animals’ jumps meet
- Common factors: jump sizes that reach two numbers
- Divisibility by 2, 5, and 10
🐸 Let’s Begin: Jumping Friends
A frog and a squirrel start at 0 on a long line. The frog jumps 2 steps at a time: 2, 4, 6, 8, 10, 12… The squirrel jumps 5 steps at a time: 5, 10, 15, 20…
“Look! We both landed on 10!” said the frog. And again on 20, 30… These meeting spots are special numbers called common multiples.
🧱 Part 1: Factors and Multiples
Arrange 18 buttons in neat rows with no button left over:
| Rows × Columns | Array |
|---|---|
| 1 × 18 | 1 long row |
| 2 × 9 | 2 rows of 9 |
| 3 × 6 | 3 rows of 6 |
So the factors of 18 are 1, 2, 3, 6, 9, 18. They divide 18 exactly, with no remainder.
And 18 is a multiple of each of these numbers.
1 is a factor of every number. Every number is a factor and a multiple of itself.
Finding all factors: the pair method
Find factors in pairs that multiply to the number. For 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. When the pairs start repeating, stop!
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
🔢 Part 2: Prime Numbers
Try making arrays of 7 marbles. You can only make 1 row of 7! Numbers like this, with exactly two factors (1 and itself), are called prime numbers.
Primes under 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
“All odd numbers are prime.” ❌ 9 = 3 × 3, 15 = 3 × 5, and 21 = 3 × 7 are not prime.
✅ 2 is the only even prime number.
🦘 Part 3: Common Multiples
A kangaroo jumps 4 at a time: 4, 8, 12, 16, 20, 24, 28, 32, 36…
A goat jumps 6 at a time: 6, 12, 18, 24, 30, 36…
They both land on 12, 24, 36, 48… These are the common multiples of 4 and 6. The first one, 12, is the smallest.
Pattern: After the first common multiple, all the others are its multiples (12, 24, 36…).
🐿️ Part 4: Common Factors
Which jump sizes can land exactly on both 18 and 30?
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 3, 6. So jumps of 1, 2, 3, or 6 reach both numbers.
Real-life use: You have 18 laddoos and 30 barfis, and you want to make identical plates with no sweets left over. You could make 1, 2, 3, or 6 plates (6 is the most). Each of the 6 plates gets 3 laddoos and 5 barfis.
✅ Part 5: Quick Divisibility Tests
| Divisible by | Rule | Examples |
|---|---|---|
| 2 | Last digit is 0, 2, 4, 6, or 8 | 34, 578, 1,000 |
| 5 | Last digit is 0 or 5 | 45, 90, 1,235 |
| 10 | Last digit is 0 | 70, 450, 8,000 |
Any number divisible by 10 is also divisible by both 2 and 5!
❌ Common Mistakes to Avoid
✅ Factors of 12: 1, 2, 3, 4, 6, 12. Multiples of 12: 12, 24, 36…
✅ They are always factors.
✅ There are infinitely many common multiples.
✅ We can’t divide by 0.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Page 164 · Hidden numbers boxFind the multiplier
Arrays for 15: 1 × 15 and 3 × 5, so the factors are 1, 3, 5, 15.
Factors of each number
(a) 10: 1, 2, 5, 10 (b) 14: 1, 2, 7, 14 (c) 13: 1, 13 (d) 20: 1, 2, 4, 5, 10, 20 (e) 25: 1, 5, 25 (f) 32: 1, 2, 4, 8, 16, 32 (g) 37: 1, 37 (h) 46: 1, 2, 23, 46 (i) 54: 1, 2, 3, 6, 9, 18, 27, 54
13 and 37 are prime because they can only be arranged in one straight row. They have only 2 factors.
Common multiples
3 and 6: 6, 12, 18, 24… These are just the multiples of 6, because 6 is itself a multiple of 3.
4 and 6: 12, 24, 36, 48, 60…
Let Us Do Q1: (a) 6, 12, 18, 24, 30 (b) 40, 80, 120, 160, 200 (c) 4, 8, 12, 16, 20 (d) 9, 18, 27, 36, 45 (e) 10, 20, 30, 40, 50 (f) 9 and 12: 36, 72, 108, 144, 180 (f) 8 and 12: 24, 48, 72, 96, 120 (g) 24, 48, 72, 96, 120 (h) 18, 36, 54, 72, 90
Notice: when one number is a multiple of the other (2 and 4, 3 and 9, 5 and 10), the common multiples are just the multiples of the bigger number.
Who reaches the food?
Which friends can he meet?
Jumps of 3: 9, 21, 39, 57 (spider, snake, deer, and monkey).
Jumps of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. So 5 is a common factor of 25, 30, 35, 50 (the friends on those spots).
Jumps of 10: 10, 20, 30, 40, 50. So 10 is a common factor of 30 and 50.
Common factors
Q5: Only 1
Q6: 16, 36, 48 (and 0). 4 is a common factor of 16, 36, and 48.
Q7: (a) 1, 2, 4 (b) 1, 2, 4 (c) 1, 2, 4 (d) 1 (e) 1 (f) 12 and 15: 1, 3 (f) 20 and 5: 1, 5 (g) 1, 3 (h) 1, 3
Notice: 1 is always a common factor. When one number divides the other (like 4 and 16), the smaller number itself is a common factor.
True or false, hunting, and the trail
Q9: Every 15th day: days 15, 30, 45, 60…
Q10: (a) The jump must divide 30 but not 25: 2, 3, 6, 10, 15, or 30 steps (1 and 5 would land on 25) (b) Common factors of 21 and 35: 1 or 7 steps
Sort by divisibility
(b) Only by 5: 75, 45, 25, 95, 55
(c) Only by 10: none, because any number divisible by 10 is also divisible by 2 and 5
(d) By 2, 5, and 10: 90, 30, 40
👨👩👧 Tips for Parents
- Arrange coins or beads in rectangles to find factors together.
- Hop on floor tiles: “If you jump 3 and I jump 4, where do we meet?”
- Ask: “Can 24 sweets be shared equally among 5 friends? Among 6?”