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Factors of 15 are the whole numbers that can divide the number 15 completely. There are 4 factors of 15 which are 1, 3, 5, and 15. The smallest factor of 15 is 1 and the greatest factor of 15 is 15 itself. The sum of all the factors of 15 is 24. The pair factors of 15 refer to those integers that give the original number 15 on multiplication with each other. (1, 15) and (3, 5) are the pair factors of 15. The prime factorization of 15 is 3 × 5, where 3 and 5 are both prime numbers.
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Key Terms: Factors of 15, Prime Factorization, Factors, Pair Factors, Remainder, Composite Number, Prime Factors, Prime Numbers
What are the Factors of 15?
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Factors of 15 refer to the list of numbers that divide the original number 15 completely.
- If a number or an integer divides 15 completely without leaving a remainder, then the number is a factor of 15.
- The factors of 15 include the pair of numbers that give the number 15 as the result when they are multiplied by each other.
15 is an odd composite number, which means, it has more than two factors. Thus, the factors of 15 are 1, 3, 5, and 15.
Factors of 15: 1, 3, 5, 10
Factors of 15
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| Chapter-Related Topics | ||
|---|---|---|
| Prime Number Formula | Co Prime Numbers | Twin Primes |
| Digits | Ordered Pairs | Real Numbers |
Pair Factors of 15
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The pair factors refer to any two numbers that, when multiplied with each other, give the original number as the product. In the case of 15, the pair factors are:
1 × 15 = 15
3 × 5 = 15
Positive Pair Factors of 15
The positive pair factors of 15 are (1, 15) and (3, 5).
| Positive Factors of 15 | Positive Pair Factors of 15 |
|---|---|
| 1 × 15 | (1, 15) |
| 3 × 5 | (3, 5) |
Negative Pair Factors of 15
The negative pair factors of 15 are (-1,-15) and (-3,-5).
| Negative Factors of 15 | Negative Pair Factors of 15 |
|---|---|
| -1 × -15 | (-1, -15) |
| -3 × -5 | (-3, -5) |
How to Calculate Factors of 15?
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15 is a two-digit odd composite number that is not divisible completely by any even number. In order to find out all the factors of 15, we need to make all possible pairs of numbers and multiply them to see if the product is 15 or not.
- Dividing 15 by 1: 15/1 = 15 and also 15/15 =1 (Thus, 1 and 15 are the factors of 15.)
- Dividing 15 by 3: 15/3 = 5 and also 15/5 = 3 (Thus, 3 and 5 are the factors of 15.)
Therefore, the maximum number of factors of 15 is 4 which are 1, 3, 5, and 15.
Read More: HCF
Prime Factorization of 15
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The prime numbers or prime factors of 15 that completely divide 15 are obtained through the prime factorization of 15. As 15 is a composite number, thus, it is divisible by one or more prime numbers.
Prime Factorization of 15
The steps to calculate the prime factors of 15 are as follows:
- Step 1: 15 is an odd number that is not divisible by the prime number 2, so we will divide it by the next prime number, i.e., 3.
15 ÷ 3 = 5
- Step 2: Dividing the remainder 5 further by 3.
5 ÷ 3 = 1.67, which is a fraction.
- Step 3: We will proceed to the next prime number, i.e. 5. Dividing 5 by 5, we get
5 ÷ 5 = 1
Thus, 1 is left at the end and we cannot proceed with the division method. Thus, the prime factorization of 15 is 3 × 5, where 3 and 5 both are prime numbers.
Read More: Is '1' a Prime Number?
Factor Tree for 15
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The prime factorization of 15 tells us about the prime factors that divide the original number 15 completely. The factor tree for 15 is as follows:
Factor Tree of 15
Solved Examples on Factors of 15
Example 1: Name the greatest common factor of 15 and 20.
Solution: We know that,
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20
We can see that the greatest number that divides both 15 and 20 is 5. Thus, the greatest common factor of 15 and 20 is 5.
Example 2: List the common factors of 15 and 16.
Solution: First we will write down the factors of both 15 and 16.
- Factors of 15: 1, 3, 5, 15
- Factors of 16: 1, 2, 4, 8, 16
From the given factors of 15 and 16, we can see that there is only one common factor between 15 and 16 which is 1.
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Things to Remember
- Factors of 15 refer to those numbers that divide the number 15 completely without leaving any remainder.
- The factors of 15 are 1, 3, 5, and 15.
- The negative factors of 15 include -1, -3, -5, and -15.
- The prime factorization of 15 is given as 3 × 5 = 3 × 5.
- There are two prime factors of 15 which are 3 and 5.
- The sum of the factors of 15 is 24.
Sample Questions
Ques. Explain the prime factorization of 15. (3 Marks)
Ans. We know that every composite number is made up of one or more prime numbers. Prime numbers which are less than 15 include 2, 3, 5, 7, 11, and 13.
Now, we will try to divide 15 with the above prime numbers.
- 15 ÷ 2 = 7.5 (A factor cannot be a decimal number)
- 15 ÷ 3 = 5 (Thus, 5 is the factor of 15)
- 15 ÷ 5 = 3,(Thus, 3 is also the factor of 15)
- 15 ÷ 7 = 2.14 (A factor cannot be a decimal number)
Thus the prime factorization of 15 is 3 x 5 = 15 or 5 x 3 = 15.
Ques. What is the greatest common divisor of 15 and 30? (2 Marks)
Ans. In order to find out the greatest common divisor of 15 and 30, we need to first write down their factors,
- Factors of 15: 1, 3, 5, 15
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
We can see that 15 is the greatest factor dividing both 15 and 30. Thus, the greatest common divisor of 15 and 30 is 15.
Ques. List the multiples of 15. (3 Marks)
Ans. The list of multiples of 15 is as follows:
- 15 x 1 = 15
- 15 x 2 = 30
- 15 x 3 = 45
- 15 x 4 = 60
- 15 x 5 = 75
- 15 x 6 = 90
- 15 x 7 = 105
- 15 x 8 = 120
- 15 x 9 = 135
- 15 x 8 = 150
Thus, the multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, and so on.
Ques. Name the factors of 15. (2 Marks)
Ans. 1, 3, 5, and 15 are the 4 factors of 15.
- Positive Factors of 15: 1, 3, 5, and 15.
- Negative Factors of 15: -1, -3, -5 and -15.
Ques. Ritik has 5 friends. He bought 15 chocolates on his birthday. Explain how should he divide the fifteen chocolates so that all his friends get an equal number of chocolates. (3 Marks)
Ans. Since Ritik has 15 chocolates to distribute among his 5 friends, we will use the concept of factors of 15 here:
AS5 is a factor of 15, dividing 15 by 5 we get 3.
15 ÷ 5 = 3
Thus, Ritik should distribute 3 chocolates each to his friends to divide the chocolates equally.
Ques. Write the common factors of the following:
(a) 15 and 5
(b) 15 and 25
(c) 15 and 24 (3 Marks)
Ans. (a) To find the common factors of 15 and 5:
-
Factors of 15: 1, 3, 5, 15
- Factors of 5: 1, 5
Thus, the common factors of 15 and 5 are 1 and 5.
(b) To find the common factors of 15 and 25:
- Factors of 15: 1, 3, 5, 15
- Factors of 25: 1, 5, 25
Thus, the common factors of 15 and 25 are 1 and 5.
(c) To find the common factors of 15 and 24:
- Factors of 15: 1, 3, 5, 15
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Thus, the common factors of 15 and 24 are 1 and 3.
Ques. What is the sum of the factors of 15? (2 Marks)
Ans. There are 4 factors of 15: 1, 3, 5, and 15.
Sum of factors of 15 will be 1 + 3 + 5 + 15 = 24.
Thus, the sum of all the factors of 15 is 24.
Ques. A box can fit up to 15 equal-sized small sweet boxes inside it. If 3 sweet boxes can be kept in one row of the big box, what will be the number of rows required to keep all 15 boxes together in the big box? (3 Marks)
Ans. We will use the concept of factors of 15 here to find out the number of rows required to keep all 15 boxes together in the big box.
- Number of sweet boxes to be kept in the big box = 15
- Number of sweet boxes in one row = 3
Dividing 15 by 3, we get 5.
It means we need 5 rows of 3 sweet boxes each to keep all 15 boxes in the big box.
Ques. Which numbers are the Prime Factors of 15? (1 Mark)
Ans. The numbers which are the prime factors of 15 are 3 and 5.
Ques. Name the Greatest Common Factor of 15 and 10. (2 Marks)
Ans. To find the greatest common factor of 15 and 10, we will first find the factors of 15 and 10:
- Factors of 15: 1, 3, 5, 15
- Factors of 10: 1, 2, 5, 10
The common factors of 15 and 10 are 1 and 5.
Thus, the greatest common factor of 15 and 10 is 5.
Ques. Write down the Common Factors of 15 and 9. (2 Marks)
Ans. The factors of 15 and 9 are:
- Factors of 15: 1, 3, 5, 15
- Factors of 9: 1, 3, 9
Thus, 1 and 3 are the common factors of 15 and 9.
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