Factors and Multiples Word Problems
Factors and multiples word problems test your ability to apply concepts of factors, multiples, HCF, and LCM to real-life situations. In Class 4, these problems involve sharing items equally, arranging objects in rows, finding common schedules, and grouping.
Understanding when to use factors (for dividing equally) and when to use multiples (for finding common events) is the key to solving these problems correctly.
What is Factors and Multiples Word Problems - Class 4 Maths (Factors and Multiples)?
Factors are numbers that divide a given number exactly (with no remainder). Use factors when you need to divide or group items equally.
Multiples are numbers obtained by multiplying a given number by 1, 2, 3, and so on. Use multiples when you need to find common events or repeated patterns.
Use HCF → when dividing into equal groups (greatest common factor)
Use LCM → when finding when events happen together (least common multiple)
Types and Properties
Types of word problems:
- Equal sharing/grouping: Use factors or HCF. Example: "Arrange 24 books equally on shelves."
- Repeated events: Use LCM. Example: "Two bells ring every 4 and 6 minutes. When do they ring together?"
- Is it possible? Check if one number is a factor of another. Example: "Can 30 students be arranged in rows of 7?"
- Finding all ways: List all factor pairs. Example: "In how many ways can 36 chairs be arranged in equal rows?"
Solved Examples
Example 1: Example 1: Equal Grouping
Problem: Meera has 48 chocolates. She wants to pack them equally into boxes. Each box must have more than 5 but less than 10 chocolates. How many chocolates per box?
Solution:
Step 1: Find factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Step 2: Factors between 5 and 10: 6 and 8
Answer: She can pack 6 or 8 chocolates per box.
Example 2: Example 2: Arranging in Rows
Problem: 36 students stand in equal rows for assembly. Find all possible arrangements.
Solution:
Step 1: Find factor pairs of 36:
1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6
Answer: Possible arrangements: 1 row of 36, 2 rows of 18, 3 rows of 12, 4 rows of 9, 6 rows of 6 (and the reverse of each).
Example 3: Example 3: Common Multiple — Bells
Problem: Two bells ring every 6 minutes and 8 minutes. They ring together at 9:00 AM. When will they ring together next?
Solution:
Step 1: Find the LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24, 30...
Multiples of 8: 8, 16, 24, 32...
Step 2: LCM = 24 minutes.
Step 3: 9:00 AM + 24 minutes = 9:24 AM
Answer: They will ring together next at 9:24 AM.
Example 4: Example 4: Is it Possible?
Problem: Can 45 mangoes be shared equally among 7 friends with none left over?
Solution:
Step 1: Check if 7 is a factor of 45.
45 ÷ 7 = 6 remainder 3
Step 2: Since there is a remainder, 7 is not a factor of 45.
Answer: No, 45 mangoes cannot be shared equally among 7 friends.
Example 5: Example 5: HCF — Equal Distribution
Problem: Aman has 18 red balls and 24 blue balls. He wants to make gift bags with the same number of red balls and the same number of blue balls in each bag, using all balls. What is the greatest number of bags he can make?
Solution:
Step 1: Find HCF of 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 6
Step 2: HCF = 6
Each bag: 18 ÷ 6 = 3 red balls, 24 ÷ 6 = 4 blue balls.
Answer: Aman can make 6 bags.
Example 6: Example 6: LCM — Buying Equal Quantities
Problem: Pencils come in packs of 6 and erasers come in packs of 4. What is the smallest number of each that Neha must buy so that she has equal numbers of pencils and erasers?
Solution:
Step 1: Find LCM of 6 and 4.
Multiples of 6: 6, 12, 18...
Multiples of 4: 4, 8, 12, 16...
Step 2: LCM = 12
Pencil packs needed: 12 ÷ 6 = 2 packs. Eraser packs needed: 12 ÷ 4 = 3 packs.
Answer: Neha must buy 12 of each (2 packs of pencils, 3 packs of erasers).
Example 7: Example 7: Common Factor Problem
Problem: Priya wants to cut a 28 cm ribbon and a 42 cm ribbon into pieces of equal length with no ribbon left. What is the longest piece she can cut?
Solution:
Step 1: Find HCF of 28 and 42.
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
HCF = 14
Answer: The longest piece is 14 cm.
Example 8: Example 8: Multiples in Daily Life
Problem: Rahul visits the library every 5 days and Dev visits every 3 days. They both visit on 1st March. When will they both visit the library on the same day again?
Solution:
Step 1: Find LCM of 5 and 3.
LCM = 15
Step 2: 1st March + 15 days = 16th March
Answer: They will both visit again on 16th March.
Example 9: Example 9: Finding the Number
Problem: A number is a common multiple of 4 and 5 and lies between 30 and 50. What is the number?
Solution:
Step 1: Common multiples of 4 and 5 are multiples of LCM(4,5) = 20.
Multiples of 20: 20, 40, 60...
Step 2: 40 lies between 30 and 50.
Answer: The number is 40.
Key Points to Remember
- Use factors when dividing items into equal groups.
- Use multiples when events repeat at regular intervals.
- HCF gives the greatest number of equal groups or the longest equal piece.
- LCM gives the earliest time two events happen together.
- Always check if the answer makes sense in the context of the problem.
- Factor pairs show all possible ways to arrange items in equal rows.
Practice Problems
- A teacher has 30 notebooks and 45 pencils to distribute equally among students. What is the greatest number of students she can give them to?
- Two traffic lights blink every 4 seconds and 5 seconds. They blink together now. After how many seconds will they blink together again?
- Aditi has 40 flowers. In how many ways can she arrange them in equal rows?
- Can 52 sweets be shared equally among 8 children with none left?
- Dev buys oranges in packs of 6 and apples in packs of 8. What is the smallest number so that he has equal oranges and apples?
- A rope of 36 m and another of 48 m are cut into equal pieces with none left. What is the longest possible piece?
Frequently Asked Questions
Q1. How do I know when to use HCF or LCM in a word problem?
Use HCF when dividing into the largest equal groups or cutting into the longest equal pieces. Use LCM when finding when two repeating events happen at the same time.
Q2. What are factors in simple words?
Factors are numbers that divide a given number exactly, with no remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12.
Q3. What are multiples in simple words?
Multiples are numbers you get when you multiply a number by 1, 2, 3, 4, and so on. For example, multiples of 5 are 5, 10, 15, 20, 25...
Q4. Can a problem use both factors and multiples?
Yes. Some problems require you to first list factors, then find multiples, or use HCF and LCM together. Read the problem carefully to decide what is needed.
Q5. How do you check if one number is a factor of another?
Divide the larger number by the smaller number. If the remainder is 0, the smaller number is a factor. For example, 6 is a factor of 42 because 42 / 6 = 7 exactly.
Q6. What is the connection between HCF and LCM?
For two numbers a and b: HCF x LCM = a x b. For example, HCF(4,6) = 2 and LCM(4,6) = 12. Check: 2 x 12 = 24 = 4 x 6.
Q7. Are factors and multiples word problems part of NCERT Class 4?
Yes, word problems on factors and multiples are an important part of the CBSE/NCERT Class 4 curriculum under the Factors and Multiples chapter.
Q8. What is the LCM of two numbers if one is a multiple of the other?
If one number is a multiple of the other, the LCM is the larger number. For example, LCM of 3 and 12 is 12, because 12 is already a multiple of 3.
