Figure it Out Exercises
1.
1. Find all multiples of 40 that lie between 310 and 410.
• The multiples of 40 are:
• So, the multiples of 40 between 310 and 410 are 320,
2.
2. Who am I? a. I am a number less than 40. One of my factors is 7. The sum of my digits is 8.
• The numbers that are multiples of 7 and are less than 40 are 7,
The only number from the list of multiples of 7 that has a sum of digits equal to 8 is
b. I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other.
Since the number has factors of 3 and 5, it must be a multiple of their least common multiple, which is 3 * 5 =
For 45, the digits are 4 and 5. The difference is 5 - 4 =
3.
3. A number for which the sum of all its factors is equal to twice the number is called a perfect number. The number 28 is a perfect number. Its factors are 1, 2, 4, 7, 14 and 28. Their sum is 56 which is twice 28. Find a perfect number between 1 and 10.
Answer:
The perfect number between 1 and 10 is 6. The factors of 6 are 1, 2, 3, and 6. Their sum is 1 + 2 + 3 + 6 =
4.
4. Find the common factors of: a. 20 and 28
Answer: 20 and 28: Common factors are 1,
b. 35 and 50
Answer: 35 and 50: Common factors are
c. 4, 8 and 12
Answer: 4, 8, and 12: Common factors are 1,
d. 5, 15 and 25
Answer: 5, 15, and 25: Common factor is
5.
5. Find any three numbers that are multiples of 25 but not multiples of 50.
Answer: Three examples are: 25, 75, 125.
6.
6. Anshu and his friends play the 'idli-vada' game with two numbers, which are both smaller than 10. The first time anybody says 'idli-vada' is after the number 50. What could the two numbers be which are assigned 'idli' and 'vada'?
Answer:• The first ‘idli-vada’ after 50 happens when the number is
• Two numbers smaller than 10 with common multiples at 60 are
7.
7. In the treasure hunting game, Grumpy has kept treasures on 28 and 70. What jump sizes will land on both the numbers?
Answer: The jump size that will land on both 28 and 70 is
8. In the diagram below, Guna has erased all the numbers except the common multiples. Find out what those numbers could be and fill in the missing numbers in the empty regions.
Answer: The common multiples could be numbers like 12, 24, 36, 48 if the numbers involved are multiples of 12.
9. Find the smallest number that is a multiple of all the numbers from 1 to 10, except for 7.
Answer: The smallest number is
10. Find the smallest number that is a multiple of all the numbers from 1 to 10.
Answer: The smallest number is