Factors

# Factors of 10 | What are the Factors and Prime Factors of 10?

Written by Prerit Jain

Updated on: 05 Dec 2023

Contents

### Factors of 10 | What are the Factors and Prime Factors of 10?

Factors of 10 are the numbers that divide the number 10 without leaving any remainder. In this article, let us understand how to find factors of 10 using the division method, what are the factors and prime factors of 10, and how to make **factor** tree along with solved examples. Scroll down to find out more.

## What Are the Factors of 10?

The factors of 10 are 1, 2, 5, and 10.

Hence, 10 has four factors. Unlike the other numbers, 10 is a composite number. If the given number is a composite number, then it has more than 2 factors, apart from 1 and the number itself. The factors of 10 has both positive and negative factors, and they are:

**Positive Factors of 10:**1, 2, 5, and 10.**Negative Factors of 10:**-1, -2, -5 and -10.**Prime Factorization of 10:**2 X 5**Prime Factors of 10:**2, 5**Sum of Factors of 10:**8**Sum of Prime factors of 10:**7

## Write Factors of 10 in Pairs

As we said, factors can be negative or positive, and the same goes for pairs as well. These pairs are the ones we get 10 as factors after we multiply them.

### Positive Pair Factor of 10

The positive pair factors of 10 are (1,10), (2,5), (5,2), (10,1).

### Negative Pair Factors of 10

The negative pair factors of 10 are (-1,-10), (-2,-5), (-5,-2), (-10,-1).

## How To Find Factors of 10 by Division Method?

To find factors of 10, we need to divide the number 10 by the sequence of the natural numbers till 10. The numbers which give the remainder are not factors of 10. Those numbers which doesn’t leave any remainder are the numbers known as factors of 10. The detailed steps to find the factors of 10 by the division method are given below:

- 10/1 = 10 (Remainder = 0)
- 10/2 = 5 (Remainder = 0)
- 10/3 = 9 (Remainder = 1)
- 10/4 = 8 (Remainder = 2)
- 10/5 = 2 (Remainder = 0)
- 10/6 = 1 (Remainder = 4)
- 10/10 = 1 (Remainder = 0)

Hence from the above division, it is clear that the numbers 1, 2, 5, and 10 don’t leave any remainder. Hence, the factors of 10 are 1, 2, 5, and 10.

## Method 2 to Find Factors of 10

Write the number 10 and any two numbers that, when multiplied together, give the result 10.**Step 1:**Using the pair factors, we are choosing 2 and 5, because 2 x 5 = 10.**Step 2:**The numbers 2 and 5 are prime numbers, so they don’t have any factors except for the number 1 and itself.**Step 3:**- 2 x 1 = 2
- 5 x 1 = 5

Since we cannot factorise the prime numbers any more, the factors of 10 are 1, 2, 5, and 10.**Step 4:**

## How To Find Prime Factorisation of 10?

The steps to find the prime factorization of 10 is given below:

**Step 1:**Firstly, we will find a small prime number that is divisible by 10. Hence we are dividing 10 with 2, which the smallest prime number.- 10 ÷ 2 = 5

**Step 2:**Since we cannot divide 5 by 2, we will choose the next smallest prime number, which is 5, to divide by 5.- 5 ÷ 5 = 1

**Step 3:**We conclude that 2 and 5 are the prime numbers of 10, because we cannot divide it further.

Hence the prime factors of 10 are 2 X 5 =10. The prime factors of 10 are 2 and 5.

## Find the Factor Tree of 10

The steps to find a factor tree of 10 is given below:

**Step 1:**Firstly, write the number 10 at the top of the factor tree**Step 2:**Now, as the part of the tree’s branches, write down the pair factors of 10 that 10 is divisible by. The pair factors we have used here is 2 and 5.**Step 3:**Since 2 and 5 are prime numbers, we cannot divide them anymore.

Circling all the branches gives us factors 2, and 5. Therefore, the prime factors of 10 using a factor tree are 2 X 5 = 10.

## Solved Examples on Factors of 10

A few solved examples on factors of 10 are given below:

**How many factors of 10 does the number 1000 have?**

The factors of 10 are 1, 2, 5, and 10.

The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.

Hence, from the above, the common factors of 10 and 1000 are 1, 2, 5, and 10.

Moreover, the factors of 1000 that can be divided by 10 are 10, 20, 40, 50, 100, 200, 250, 500, and 1000.

**Which answer choice contains all the factors of 10?****A) 1, 2, 5, 10B) 2, 5C) 1, 10D) 1, 2, 5**

**Option A contains all the factors of 10 as the factors of 10 are 1, 2, 5, and 10.**

Answer:

Answer:

**What’s the highest common factor of 10 and 30?**The factors of 10 are 1, 2, 5, and 10.

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

Hence, from the above, the common factors of 10 and 30 are 1, 2, 3, 5, and 10.

The highest common factor of 10 and 30 is 10.

**What’s the highest common factor of 10 and 5?**The factors of 10 are 1, 2, 5, and 10.

The factors of 5 are 1 and 5.

From the above, the common factors of 10 and 5 are 1 and 5.

The highest common factor of 10 and 5 is 5.

**What are the highest common factor of 4 and 10?**

Factors of 4 = 1, 2, and 4.

Factors of 10 = 1, 2, 5, and 10.

From the above, the common factors of 4 and 10 are 1 and 2.

Hence the highest common factor between 4 and 10 is 2.

**What are the common factors of 10 and 15?**

The factors of 10 are 1, 2, 5, and 10.

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

From the above, the common factors of 10 and 15 are 1, 2, and 5.

The highest common factor of 10 and 15 is 5.

## FAQs on Factors of 10

**What are the factors and prime factors of 10?**The factors of 10 are 1, 2, 5, and 10.

The prime factors of 10 are 2 and 5.

**What is the Sum of all the Factors of 10?**The factors of 10 are 1, 2, 5, and 10.

Therefore, adding all the factors of 10 =1 + 2 + 5 + 10 = 18.

Hence 18 is the sum of factors of 10.

**What are the composite factors of 10?**

Any number which has more than 2 factors is known as a composite number.

10 is the only composite factor of 10.

**What are the positive factors of 10?**

1, 2, 5, and 10 are the positive factors of 10.

**What are the factors of 10 in pairs?**

(1, 10) and (2, 5) are the pairs of factors of 10.

**What are the factors of -10?**

1, 2, 5, and 10 are the factors of -10.

**Conclusion**

So, that’s all about factors of 10. We hope all your doubts are solved and you have a much better understanding of the factors of 10 But if you still have any doubts or concerns, you can share them with us in the comment section and we will surely respond soon with solutions to them.

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Written by

Prerit Jain