Factors of 30
Factors of 30 are the numbers, which gives the result as 30 when multiplied together in pair of two. We can also say factors are the numbers that divide a number completely, leaving zero as a remainder. The factors of 30 can be positive or negative, but they cannot be a decimal or fraction. For example, the factor of 30 can be (1, 30) or (-1, -30). If we multiply the pair of negative numbers, such as multiplying -1 and -30, it will result in an original number 30. In this article, we are going to learn the pair factors and the prime factors of 30 using the division method and the prime factorization method.
What are the Factors of 30?
The factors of 30 are the numbers that divide 30 exactly without leaving a remainder. As the number 30 is an even composite number, it has factors other than 1 and 30. Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30. Prime Factorization of 30: 2 × 3 × 5 |
Pair Factors of Thirty
A pair of numbers, which are multiplied together resulting in an original number 30 is called the pair factors of Thirty. As discussed above, the pair factors of Thirty can be positive or negative. The positive and negative pair factors of Thirty are given below.
Positive Pair Factors of Thirty:
Positive Factors of Thirty | Positive Pair Factors of Thirty |
1 × 30 | (1, 30) |
2 × 15 | (2, 15) |
3 × 10 | (3, 10) |
5 × 6 | (5, 6) |
Negative Pair Factors of Thirty:
Negative Factors of Thirty | Negative Pair Factors of Thirty |
-1 × -30 | (-1, -30) |
-2 × -15 | (-2, -15) |
-3 × -10 | (-3, -10) |
-5 × -6 | (-5, -6) |
Therefore, the positive pair factors of Thirty are (1, 30), (2, 15), (3, 10) and (5, 6) and the negative pair factors of Thirty are (-1, -30), (-2, -15), (-3, -10) and (-5, -6).
Factors of 30 by Division Method
In the division method, the factors of Thirty can be found by dividing the number 30 by different integers. If the integer divides 30 exactly, then those integers are the factors of Thirty. Now, let us discuss how to find the factors of Thirty using the division method.
Now, let us start dividing 30 by 1, and then continue with the consecutive integers.
- 30/1 = 30 (Factor = 1 and Remainder = 0)
- 30/2 = 15 (Factor = 2 and Remainder = 0)
- 30/3 = 10 (Factor = 3 and Remainder = 0)
- 30/5 = 6 (Factor = 5 and Remainder = 0)
- 30/6 = 5 (Factor = 6 and Remainder = 0)
- 30/10 = 3 (Factor = 10 and Remainder = 0)
- 30/15 = 2 (Factor = 15 and Remainder = 0)
- 30/30 = 1 (Factor = 30 and Remainder = 0)
If you divide 30 by any numbers other than 1, 2, 3, 5, 6, 10, 15 and 30, it leaves a remainder. Hence, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Prime Factorization of 30
The number 30 is a composite number. Now let us find the prime factors of it.
- The first step is to divide the number 30 with the smallest prime number, i.e. 2.
30 ÷ 2 = 15
15 ÷ 2 = 7.5; factor cannot be a fraction.
- Now, proceed to the next prime number, i.e. 3 and divide 15 with it.
15 ÷ 3 = 5
- Again, if we divide 5 by 3, we get a fraction number, which we cannot consider as a factor.
- Therefore, we will move to the next prime number, which is 5.
5 ÷ 5 = 1
- We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorisation of 30 is 2 × 3 × 5, where 2, 3 and 5 are the prime numbers.
Examples
Example 1:
Find the common factors of Thirty and 31.
Solution:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
The factors of 31 are 1 and 31.
Thus, the common factor of Thirty and 31 is 1 only, as 31 is a prime number.
Example 2:
Find the common factors of Thirty and 29.
Solution:
Factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30.
Factors of 29 = 1 and 29.
Hence, the common factor of Thirty and 29 is 1.
Frequently Asked Questions on Factors of Thirty
Q1 What are the factors of Thirty?
Ans. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Q2 What is the prime factorization of Thirty?
Ans. The prime factorization of 30 is 2 × 3 × 5.
Q3 What are the positive pair factors of Thirty?
Ans. The positive pair factors of Thirty are (1, 30), (2, 15), (3, 10) and (5, 6).
Q4 What are the negative pair factors of Thirty?
Ans. The negative pair factors of Thirty are (-1, -30), (-2, -15), (-3, -10) and (-5, -6).
Q5 Is 15 a factor of Thirty?
Ans. Yes, 15 is a factor of Thirty. As 15 divides 30 exactly without leaving a remainder, 15 is a factor of 30.
Category: Maths