Jump Jackpot
Jumpy and Grumpy play a game.
• Grumpy places a treasure on some number. For example, he may place it on 24. • Jumpy chooses a jump size. If he chooses 4, then he has to jump only on multiples of 4, starting at 0.
• Jumpy gets the treasure if he lands on the number where Grumpy placed it.
Which jump sizes will get Jumpy to land on 24?
If he chooses 4: Jumpy lands on 4 → 8 → 12 → 16 → 20 → 24 → 28 → ...
Other successful jump sizes are 2, 3,
What about the jump of sizes 1 and 24? Yes, they also will land on 24.
The numbers 1, 2, 3, 4, 6, 8, 12, 24 all divide 24 exactly. Recall that such numbers are called
Grumpy increases the level of the game. Two treasures are kept on two different numbers. Jumpy has to choose a jump size and stick to it. Jumpy gets the treasures only if he lands on both the numbers with the chosen jump size. As before, Jumpy starts at 0.
Grumpy has kept the treasures on 14 and 36. And, Jumpy chooses a jump size of 7.
Will Jumpy land on both the treasures? Starting from 0, he jumps to 7 → 14 → 21 → 28 → 35 → 42 … We see that he landed on
The factors of 14 are: 1, 2, 7, 14. So, these jump sizes will land on 14.
The factors of 36 are: 1, 2, 3, 4, 6, 9,
So, the jump sizes of
The jump sizes using which both the treasures can be reached are the common factors of the two numbers where the treasures are placed.
What jump size can reach both 15 and 30? There are multiple jump sizes possible. Try to find them all.
Look at the table below. What do you notice?
In the table, 1. Is there anything common among the shaded numbers?
Answer They’re all multiples of
2. Is there anything common among the circled numbers?
Answer They’re all multiples of
3. Which numbers are both shaded and circled? What are these numbers called? Answer These are called