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Factors

What Are the Factors of 30? | Factor Tree of 30 | Prime Factors of 30

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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What Are the Factors of 30? | Factor Tree of 30 | Prime Factors of 30

What Are the Factors of 30? | Factor Tree of 30 | Prime Factors of 30

Factors of 30: A list of integers that can be divided by 30 with 0 as a remainder is known as 30 factors. The 30 factor has both negative and positive numbers. A number that is a factor of 30 with a negative sign is known as a negative factor of 30. Also, the numbers which are factors of 30 with positive signs are known as positive factors of 30. In this blog, let us understand how to find factors of 30 along with solved examples. Scroll down to find out more.

What Are the Factors of 30?

Factors are the numbers that divide the original number without leaving any remainder. In the case of 30, the numbers 1, 2, 3, 5, 6, 10, 15, and 30 are the numbers that divide the number 30 without leaving any remainder. Therefore, factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Since 30 is a composite number, it has more than two factors, which are both positive and negative. The positive and negative factors of 30 are given below:

  • 1, 2, 3, 5, 6, 10, 15, and 30 are positive factors of 30.
  • -1, -2, -3, -5, -6, -10, -15, and -30 are negative factors of 30.

Write Factors of 30 in Pairs?

The factors of 30 can be written in two pairs, namely positive pairs and negative pairs. The positive and negative pairs of 30 are given below:

Positive Pair Factors of 30

Below are the positive pair factors of 30:

Positive Pair Factors of 30

Negative Pair Factors of 30

Below are the negative pair factors of 30:

Negative Pair Factors of 30

How To Find Factors of 30 Through Division Method?

You can find factors of 30 through the division method. For that, you will have to divide the number 30 by the sequence of natural numbers up to 30. A number that is divided by 30, and doesn’t leave any remainder, is the number that is considered a factor of 30. The details on how to find the factors of number 30 are given below:

  • 30 ÷ 1 = 30
  • 30 ÷ 2 = 15
  • 30 ÷ 3 = 10
  • 30 ÷ 5 = 6
  • 30 ÷ 6 = 5
  • 30 ÷ 10 = 3
  • 30 ÷ 15 = 2
  • 30 ÷ 30 = 1

As we can see, only the above numbers don’t leave a remainder after division, so that means 1, 2, 3, 5, 6, 10, 15, and 30 are the factors of 30.

What Is the Prime Factorisation of 30?

We can also find prime factors of 30 through prime factorization. Let’s see the steps below for the prime factorization of 30.

  • Step 1: Divide the number 30 by the least prime number. Hence, the least prime number that is divisible by 30 is 2.
    30/2 = 15
  • Step 2: When 30 is divided by 2, we will get the number 15. Now, we will divide it again by the smallest prime number that 15 can be divided by, i.e 3.
    15/3 = 5
  • Step 3: Since 5 is a prime number, we can only divide it by 5.
    5/5 = 1

Therefore, 2 X 3 X 5 = 30. So, 2, 3, and 5 are the prime factors of 30.

Prime Factorization of 30

Write the Factor Tree of 30.

We can also find the prime factors of the number 30 using the factor tree method. The steps to finding prime factors of 30 using the factor tree method are given below:

  • Step 1: Place the number 30 at the top of the factor tree.
  • Step 2: Now, as the tree branches, we will write down the pair factors of 30 we can divide 30 by Here we are using the pair factor 3, 15 as the first branch of 30.
  • Step 3: Since 3 is a prime number, we can no longer divide it. But, we can divide 15 by 2 and 5.
  • Step 4: As 2 and 5 are prime numbers, we cannot further separate them. 

Hence, circling all the branches gives us factors 2, 3, and 5. Therefore, the prime factors of 30 using a factor tree are 2 X 3 X 5 = 30.

The factor tree of 30 is given below:

Factor tree of 30

List All the Factors of 30 From Least to Greatest

The factors of 30 are 3, 5, 10, 15, 30, 1, 2, and 6.
Now, let’s arrange the factors of 30 from least to great or in increasing order.
Hence, factors of 30 in increasing order will be:
1, 2, 3, 5, 6, 10, 15, and 30.

Solved Examples on Factors of 30

Some of the solved examples on factors of 30 are given below:

What is the sum of all the Factors of 30?
The factors number 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Hence adding 1 + 2 + 3 + 5 + 6 + 10 + 15 +30 = 72
The sum of factors of 30 is 72.

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

What’s the highest common factor of 45 and 30?
Factors of 45: 1, 3, 5, 9, 15, and 45.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.
Hence the common factors of 45 and 30 are 1, 3, 5, and 15.
Therefore the highest common factor of 45 and 30 is 15.

What’s the highest common factor of 50 and 30?
Factors of 50: 1, 2, 5, 10, 25, and 50.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.
From the above, the common factors of 50 and 30 are 1, 2, 5, and 10.
Hence the highest common factor of 50 and 30 is 10.

FAQs on Factors of 30

The frequently asked questions on 30 factors are given below:

List all the factors of 30.
1, 2, 3, 5, 6, 10, 15, and 30 are factors of 30.

What are the composite factors of 30?
6, 10, 15, and 30 are the only composite factors of 30.

What are the factors of 30 in pairs?
(1, 30), (2, 15), (3, 10), and (5, 6) are the pairs of factors of 30.

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

What are the common factors of 30 and 100?
Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 10
Hence, the common factors of 30 and 100 are 1, 2, and 5.
Also, the least common factor of 30 and 100 is 1.

What are the common factors of 30 and 42?
Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30
Factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42
Hence, the common factors of 30 and 42 are 1, 2, 3, and 6.
Also, the least common factor of 30 and 42 is 1.

That’s all about factors of 30 for now. We hope this blog has been useful for you and you were able to learn a lot. If you still have any doubts popping on your mind, feel free to comment below and we will reply with answers as soon as possible.

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