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Factors of 10 are the numbers that divide the number 10 uniformly. There are four factors of 10 which are 1, 2, 5, and 10 with 10 being the largest factor of itself. The sum of all the factors of 10 is 18. Pair Factors of 10 are the whole numbers that give the product as 10 when multiplied together in pair. The factors of 10 in pairs are (1, 10) and (2, 5). We can calculate the factors of 10 easily with the help of prime factorization, The prime factorization of 10 is 2 x 5 with 2 and 5 being the only two prime factors of 10.
Key Terms: Factors of 10, Factors Pairs, Prime Factors, Prime Factorization, Composite Number, Factors, Remainder, Integer
What are Factors of 10?
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Factors of 10 are the numbers that divide 10 completely. It means the numbers that do not leave the remainder on division with 10 are called the factors of 10. Thus, the factors of 10 are 1, 2, 5, and 10 which on dividing 10 leaves the remainder as 0.
Factors of 10 = 1, 2, 5, 10
Factors of 10
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How to Calculate Factors of 10?
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Factors of 10 are the numbers which when multiplied together, give the product as 10. In order to calculate the factors of 10, we will find the pair of two numbers whose product is equal to 10.
- 2 x 5 = 10
- 10 x 1 = 10
Thus, we have only two pairs of numbers that give us the product 10. Hence, the factors of 10 are 1, 2, 5, and 10.
Read More: HCF
Factors of 10 by Prime Factorization
Prime Factorization is defined as a way of expressing a number as a product of its prime factors. We know that 10 is a composite number which means that it can be written as the product of prime numbers.
Prime Factorization of 10
In order to calculate the prime factors of 10, we will break down the number 10 into the set of primes which when multiplied together gives the result of 10.
2 x 5 = 10
2 and 5 are only prime numbers that divide 10 and give the product as 10 on multiplication. Thus, the prime factorization of 10 can be expressed as 10 = 2 × 5.
Read More: Co Prime Numbers
Factors of 10 in Pairs
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Factor Pairs of 10 are the pair of numbers that give 10 when multiplied together. In order to find the pair factors for 10, we need to multiply the two numbers to get the original number as 10. The pair factors of a number can be positive as well as negative.
- Positive Pair Factors of 10: (1, 10), (2, 5), (5, 2), and (10, 1).
- Negative Pair Factors of 10: (-1, -10), (-2, -5), (-5, -2), and (-10, -1).
| Positive Pairs Factors of 10 | Negative Pairs Factors of 10 |
|---|---|
| 1 × 10 = 10; (1, 10) | (-1) × (-10) = 10; (-1, -10) |
| 2 × 5 = 10; (2, 5) | (-2) × (-5) = 10; (-2, -5) |
| 5 × 2 = 10; (5, 2) | (-5) × (-2) = 10; (-5, -2) |
| 10 × 1 = 10; (10, 1) | (-10) × (-1) = 10; (-10, -1) |
Read More: Twin Primes
Solved Examples on Factors of 10
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Example 1: Are there any common factors of the numbers 9 and 10?
Solution: Writing down all the factors of 10, we get
- Factors of 9: 1, 3, 9
- Factors of 10: 1, 2, 5, 10
Thus, there is only one common factor of 9 and 10 which is 1.
Example 2: Name the Greatest Common Factor of 10 and 6.
Solution: The factors of 10 and 6 are as follows:
- Factors of 10: 1, 2, 5, 10
- Factors of 6: 1, 2, 3, 6
The common factors of 10 and 6 are 1 and 2. Thus, the greatest common factor of 10 and 6 is 2.
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Things to Remember
- Factors of 10 are the numbers that divide 10 completely with zero as the remainder.
- There are only four factors of 10.
- 1, 2, 5, and 10 are the factors of 10.
- Factors of 10 in pairs are (1, 10) and (2, 5).
- The sum of all the factors of 10 is equal to 18.
- The prime factorization of 10 is 2 x 5 where 2 and 5 are the two prime factors of 10.
Sample Questions
Ques. What are the common factors of 10 and 20? (2 Marks)
Ans. The factors of 10 and 20 are
- Factors of 10: 1, 2, 5, and 10
- Factors of 20: 1, 2, 4, 5, 10, and 20
Thus, the common factors of 10 and 20 are 1, 2, 5, and 10
Ques. List the prime factors of 10. (2 Marks)
Ans. The prime factors of a number are those numbers that divide the number completely leaving zero as the remainder and they are prime in nature. Thus, there are only two prime factors of 10 which are 2 and 5.
Ques. What are some important facts about factors? (3 Marks)
Ans. Some important facts about factors are as follows:
- Factors are always whole numbers or integers and never decimals or fractions.
- Every even number will have the number 2 as its factor.
- The numbers that end with the number 5 will have 5 as their factor.
- Numbers greater than 0 and ending with a 0 will have numbers 2, 5, and 10 as their factors.
Ques. What are the factors? (1 Mark)
Ans. Factors of a number are the numbers that divide a number evenly leaving zero as the remainder. A number can have two or more than two factors.
Ques. List the multiples of 10. (2 Marks)
Ans. The multiples of 10 are infinite, so, here are the first 10 multiples of 10:
- 10 × 1 = 10
- 10 × 2 = 20
- 10 × 3 = 30
- 10 × 4 = 40
- 10 × 5 = 50
- 10 × 6 = 60
- 10 × 7 = 70
- 10 × 8 = 80
- 10 × 9 = 90
- 10 × 10 = 100
Ques. How many common factors do 10 and 100 have? (2 Marks)
Ans. We know that
- 10 has 4 factors which are 1, 2, 5, and 10.
- 100 has 9 factors which are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
We can see that there are four common factors of 10 and 100 which are 1, 2, 5, and 10.
Ques. What is the sum of the factors of 10? (2 Marks)
Ans. There are only four factors of 10 which are:
Factors of 10 = 1, 2, 5, 10
Adding all these factors, we get
1 + 2 + 5 + 10 = 18
Thus, the sum of the factors of 10 is 18.
Ques. What are factors of 10? (2 Marks)
Ans. Factors of 10 are the numbers that divide the original number 10 uniformly. They are the whole numbers that when multiplied together produce the original given number. Factors of 10 are 1, 2, 5, and 10.
Ques. Can 10 have negative factor pairs? (2 Marks)
Ans. Yes. It is possible to have negative pair factors too as the product of two negative numbers also gives a positive number. The negative factor pairs of 10 are (-1,-10) and (-2,-5).
Ques. List the positive and negative pair factors of 10. (2 Marks)
Ans. The positive and negative pair factors of 10 are:
- Positive Pair Factors: (1,10) and (2,5)
- Negative Pair Factors: (-1,-10) and (-2,-5)
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