Students will surely benefit from the factors and multiples questions offered here along with complete solutions in order to obtain a better knowledge of the concept. Factors and multiples are fundamental concepts that are taught in both primary and secondary school. Factors and multiples questions appear in almost every board test as well as competitive examination. These questions can be used by students to get a rapid overview of the topics and to practice them in order to improve their knowledge of the subject. You can also compare your answer with the solutions provided on our page. To understand more about factors and multiples, click here.
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What are Factors and Multiples? Multiples and factors are related to one another. A number’s factor is the number that totally divides the given number without leaving any remainder. We can express any integer using the formula a × b = c. We say c is a multiple of a and b in this case. Also, a and b are factors of c, according to the definition of factors and multiples, because c is divisible by both a and b. For instance, 5 × 3 = 15, which means that 5 and 3 are factors of 15 and that 15 is a multiple of 3 and 5. |
Factors and Multiples Questions with Solutions
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How to Find the Factors of a Number? Step 1: Consider two numbers such that their product results in 35. Step 2: Let’s say we take 7 and 5 as the numbers. Step 3: Here 35 is divisible by 7 and 5 without leaving any remainder. Step 4: So, 35 is factored in as 35 = 7 × 5. Note: The factor of the respective number is always 1 and the number itself. |
1. What are the factors of 9?
Solution:
The factors of 9 are the numbers which when multiplied together results in the number 9.
Thus,
1 × 9 = 9
3 × 3 = 9
9 × 1 = 9
Hence, the factors of 9 are 1, 3 and 9.
2. What is the sum of factors of 12?
Solution:
The factors of 12 can be found as follows:
1 × 12 = 12 or 12 × 1 = 12
2 × 6 = 12 or 6 × 2 = 12
3 × 4 = 12 or 4 × 3 = 12
Hence, the factors of 12 are 1, 2, 3, 4, 6, 12.
Therefore, the sum of factors of 12 = 1 + 2 + 3 + 4 + 6 + 12 = 28.
3. Find the common factors of 30 and 45.
Solution:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
The factors of 45 are 1, 3, 5, 9, 15 and 45
Hence, the common factors of 30 and 45 are 1, 3, 5, and 15.
4. What is the greatest common factor of 3 and 15.
Solution:
The factors of 3 are 1 and 3.
The factors of 15 are 1, 3, 5 and 15.
Therefore, the greatest common factor of 3 and 15 is 3.
5. Find the greatest common factor of 20 and 6?
Solution:
The factors of 6 are 1, 2, 3 and 6.
The factors of 20 are 1, 2, 4, 5, 10 and 20.
Thus the greatest common factor of 6 and 20 is 2.
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How to Find Multiples? The numbers we get when multiplying a number by a whole number are called multiples of that number. Let’s use the same scenario as in number 35. What is the best way to find multiples of 35? All the numbers that follow from multiplying 35 by another whole number are known as multiples of 35. For example, 35, 140, and 210 are multiples of 35. Also, the skip counting method is one of the most straightforward methods for determining the multiples of any given number. |
6. Find the first 10 multiples of 10.
Solution:
As we know, the multiples of a number are the numbers, which are obtained by multiplying the given number with the whole numbers.
Hence, the first 10 multiples of 10 are found as follows:
1 × 10 = 10
2 × 10 = 20
3 × 10 = 30
4 × 10 = 40
5 × 10 = 50
6 × 10 = 60
7 × 10 = 70
8 × 10 = 80
9 × 10 = 90
10 × 10 = 100
Therefore, the first 10 multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
7. What are the first five multiples of 7?
Solution:
To find: First five multiples of 7.
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Multiples of 7 through Multiplication |
Multiples of 7 through Addition |
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1 × 7 = 7 |
7 |
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2 × 7 = 14 |
7 + 7 = 14 |
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3 × 7 = 21 |
7 + 7 + 7 = 21 |
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4 × 7 = 28 |
7 + 7 + 7 + 7 = 28 |
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5 × 7 = 35 |
7 + 7 + 7 + 7 + 7 = 35 |
Therefore, the first 5 multiples of 7 are 7, 14, 21, 28 and 35.
8. Find the least common multiple of 12 and 18.
Solution:
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, …
The multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, …
Thus, the least common multiple of 12 and 18 is 36.
9. Find the common multiples of 3 and 5.
Solution:
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ..
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, …
Therefore, the common multiples of 3 and 5 are 15, 30, 45, 60, and so on.
10. What are the first three common multiples 4 and 8?
Solution:
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
The multiples of 8 are 8 ,16, 24, 32, 40, 48, 56, 64, 72, 80, …
Hence, the first 3 common multiples of 8, 16 and 24.
Explore More Articles:
- Factors Questions
- Multiples Questions
- LCM Questions
- Addition and Subtraction Questions
- Permutation and Combination Questions
- Rational Numbers Questions
Practice Questions
Solve the following factors and multiples questions:
- Find the least common multiple of 14 and 26.
- Find the greatest common factor of 32 and 64.
- Determine the first three common multiples of 6 and 30.
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