Factors of 30 include the numbers that can be evenly divided into 30 without leaving a remainder. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. These factors are obtained by dividing 30 by each number, resulting in whole numbers. These are useful in various mathematical calculations and essential in determining common multiples and factors of other numbers.
What are the Factors of 30?
Factors of 30 include the numbers that can be evenly divided into 30 without leaving a remainder.
- Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30
- Negative Factors of 30: -1, -2, -3, -5, -6, -10, -15 and -30
- Prime Factors of 30: 2, 3, 5
- Prime Factorization of 30: 2 × 3 × 5 = 2 × 3 × 5
- The sum of Factors of 30: 72
Pair Factors of 30
The pair factors of 30 are the combinations of two numbers that, when multiplied together, result in 30. For 30, the pair factors are (1, 30), (2, 15), (3, 10), and (5, 6).
These pairs are obtained by dividing 30 by various numbers and identifying the pairs that give a product of 30.
Pair factors are useful in mathematics for finding factors and determining prime numbers, as well as in various real-life applications such as calculating dimensions or distributing items into equal groups.
How many Prime Factors of 30?
We discover that 30 has a total of 3 prime factors when we add up the number of prime numbers mentioned above.
Positive Pair Factors of 30:
| Positive Factors of 30 | Positive Pair Factors of 30 |
| 1 × 30 | (1, 30) |
| 2 × 15 | (2, 15) |
| 3 × 10 | (3, 10) |
| 5 × 6 | (5, 6) |
Negative Pair Factors of 30:
| Negative Factors of 30 | Negative Pair Factors of 30 |
| -1 × -30 | (-1, -30) |
| -2 × -15 | (-2, -15) |
| -3 × -10 | (-3, -10) |
| -5 × -6 | (-5, -6) |
Factors of 30 by Division Method
| Division | Factor | Remainder |
| 30 ÷ 1 | 1 | 0 |
| 30 ÷ 2 | 2 | 0 |
| 30 ÷ 3 | 3 | 0 |
| 30 ÷ 5 | 5 | 0 |
| 30 ÷ 6 | 6 | 0 |
| 30 ÷ 10 | 10 | 0 |
| 30 ÷ 15 | 15 | 0 |
| 30 ÷ 30 | 30 | 0 |
To find the factors of 30 using the division method, we divide 30 by the smallest prime number, 2. We continue dividing by prime numbers until we reach the square root 30.
Now, divide 30 by 1 and then continue with the consecutive integers.
The factors obtained through this process are 1, 2, 3, 5, 6, 10, 15, and 30.
Factor Tree of 30
How To Calculate Factors of 30?
To calculate the factors of 30, you need to find all the numbers that divide evenly into 30 without leaving a remainder. Here’s a step-by-step process:
Start by listing the numbers from 1 to 30: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Check each number to see if it divides evenly into 30. To do this, divide 30 by each number and see if the remainder is 0.
The factors of 30 are the numbers that divide evenly into it. In this case, the factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
So, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Factors of 30 by Prime Factorization
Begin by finding the prime factors of 30. Prime factors are the prime numbers that divide evenly into a given number.
The prime factorization of 30 can be found by dividing it by prime numbers in ascending order: 2, 3, 5, 7, 11, and so on.
Start with 2: 30 ÷ 2 = 15
Now, divide 15 by 2 again: 15 ÷ 2 = 7.5
Since 7.5 is not an integer, move on to the next prime number, which is 3: 15 ÷ 3 = 5
5 is a prime number, so the prime factors of 30 are 2, 3, and 5.
Write the prime factors in ascending order: 2, 3, 5
Factors of 30 in Pairs
To find the factors of 30 in pairs, you can pair up the factors by multiplying them together to obtain the product of 30. Here are the pairs of factors for 30:
| The product form of 30 | Pair factor |
| 1 × 30 = 30 | (1,30) |
| 2 × 15= 30 | (2,15) |
| 3 × 10 = 30 | (3,10) |
| 5 × 6 = 30 | (5,6) |
| -1 × -30 = 30 | (-1,-30) |
| -2 × -15 = 30 | (-2,-15) |
| -3 × -10 = 30 | (-3,-10) |
| -5 × -6 = 30 | (-5,-6) |
Example 1:
Anaya has (-6) as one of the factors of 30. How will she get the other factor?
Solution:
If Jill knows that (-6) is one of the factors of 30, she can find the other factor by dividing 30 by (-6).
Dividing 30 by (-6) will give the quotient, which is the other factor:
30 ÷ (-6) = -5
So, the other factor is -5. Therefore, if Jill has (-6) as one of the factors of 30, the other factor is -5.
Find the Least Common Multiple and Greatest Common Factor (GCF) of 30 and 36.
Example 2:
Find the common factors of 24 and 36.
Solution:
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12.
Example 3:
Find the common factors of 30 and 54
Solution:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The common factors of 30 and 54 are 1, 2, 3, and 6.
30 has more than two factors, making it a composite rather than a prime number.
Composite number: Positive integers with more than two factors are mixed numbers.
Prime Number: – An integer that may be divided only by itself and 1.
30 is NOT a square number
18 has a square root of 5.48.
30 squared equals 900.
I hope you solve the factors of 30. Now attempt to determine the factors of the following integers independently. 1, 2, 3, 5, 6, 10, 15, 30 FACTORS OF 30. In addition to factors of 30, there are other considerations listed below.
That’s right—15 is a factor of 30. 15 is a factor of 30 because it divides 30 perfectly without leaving a remainder.
