# Factors of 30: Find the Prime, Pair, & Common Factors

May 22, 2023

Factors of 30 are numbers that divide evenly into 30 without leaving a remainder. Let’s delve into the factors and uncover their properties.

To identify the factors of 30, we need to find all the numbers that can divide 30 without any remainder. Starting with the number 1, we see that 1 is a factor of every number, including 30. Moving on, we find that 2 does not evenly divide 30 since 30 divided by 2 is 15 with a remainder. Similarly, 3 is a factor of 30 because 30 divided by 3 is 10 without any remainder.

Continuing our exploration, we encounter the number 4. Dividing 30 by 4 yields a quotient of 7 with a remainder, indicating that 4 is not a factor of 30. Similarly, we find that 5 divides 30 evenly, as 30 divided by 5 is 6 without any remainder.

Examining the number 6, we discover that 6 is indeed a factor of 30 since it divides evenly into it. Dividing 30 by 6 results in a quotient of 5 with no remainder. This showcases the fact that factors can be smaller than the number itself, emphasizing the concept of proper factors.

As we progress, we reach the number 7. Dividing 30 by 7 gives us a quotient of 4 with a remainder, indicating that 7 is not a factor of 30. Similarly, we find that 8, 9, and 10 are not factors of 30, as they do not divide evenly into them.

Upon reaching the number 10, we notice an interesting property of factors. Since 10 divides 30 evenly, we can conclude that any factor of 10 is also a factor of 30. In this case, the factors of 10 are 1, 2, 5, and 10, all of which are factors of 30 as well.

Continuing our exploration, we find that 15 is a factor of 30 since 30 divided by 15 is 2 without a remainder. This reveals another intriguing property: factors can come in pairs. In the case of 30, the pairs of factors are (1, 30), (2, 15), (3, 10), and (5, 6). These pairs illustrate the concept of factor pairs, where two factors multiply together to give the original number.

By examining the factors of 30, we realize that they are the numbers that can divide 30 evenly, leaving no remainder. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. These factors showcase the various ways in which 30 can be divided, highlighting its divisibility properties.

## What are the factors of 30?

Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.

## Prime Factorization of 30

The prime factors are the prime numbers that, when multiplied together, give the number 30. To determine the prime factors of 30, we can follow a systematic approach.

First, we divide 30 by the smallest prime number, which is 2. Since 30 is divisible by 2, we obtain 30 ÷ 2 = 15. Now, we continue the process with the quotient, which is 15.

Next, we check if 15 is divisible by 2 again. However, 15 is an odd number and not divisible by 2. We move on to the next prime number, which is 3. Since 15 is divisible by 3, we have 15 ÷ 3 = 5.

Now, we have reached a prime number, 5. Since 5 is a prime number itself, we cannot divide it further.

Therefore, the prime factors of 30 are 2, 3, and 5. These prime factors, when multiplied together, give the original number 30. In other words, we can express 30 as a product of its prime factors: 2 × 3 × 5.

Understanding the prime factors of a number is useful in various mathematical applications, such as simplifying fractions, finding common factors, and determining the prime factorization of a number.

## What are the Pair Factors of 30?

The pair factors are the pairs of numbers that, when multiplied together, result in the number 30. To find the pair factors, we can list all the possible combinations of numbers that multiply to give 30.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Using these factors, we can find the pair factors of 30:

1 × 30 = 30
2 × 15 = 30
3 × 10 = 30
5 × 6 = 30

Therefore, the pair factors of 30 are (1, 30), (2, 15), (3, 10), and (5, 6). These pairs of numbers, when multiplied together, equal 30. It’s important to note that the order of the factors in the pair doesn’t matter, so (1, 30) is the same as (30, 1).

## What are the common factors of 30?

The common factors are the numbers that evenly divide 30 without leaving a remainder. To find the common factors, we need to identify the factors that are shared by 30 and another number.

The 30 factors are 1, 2, 3, 5, 6, 10, 15, and 30.

Now, let’s consider some numbers and determine their common factors with 30:

1. 30 and 15: 1, 3, 5, 15
2. 30 and 10: 1, 2, 5, 10
3. 30 and 20: 1, 2, 5, 10
4. 30 and 25: 1, 5

From the above comparisons, we can identify the common factors of 30 as 1, 2, 5, and 10. These numbers divide both 30 and the respective numbers without any remainder.

## Solved factors of 30 with examples

1. What are the factors of 30?
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

2. Is 30 a prime number?
No, 30 is not a prime number because it has factors other than 1 and itself.

3. How many factors does 30 have?
30 has a total of 8 factors.

4. What is the largest factor of 30?
The largest factor of 30 is 30 itself.

5. What are the prime factors of 30?
The prime factors of 30 are 2, 3, and 5.

6. Is 30 a perfect square?
No, 30 is not a perfect square because it cannot be expressed as the square of an integer.

7. Can 30 be divided evenly by 7?
No, 30 cannot be divided evenly by 7.

8. What is the sum of the factors of 30?
The sum of the factors of 30 is 72.

9. What is the product of the factors of 30?
The product of the factors of 30 is 900.

10. Can 30 be expressed as a product of prime numbers?
Yes, the prime factorization of 30 is 2 * 3 * 5, where 2, 3, and 5 are prime numbers.

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