Factors of 10

Factors of 10 are 1, 2, 5, and 10. These numbers in a certain pair can be multiplied together to result in the number 10. These integers can divide 10 without leaving any remainder. Understanding factors helps in grasping the basic building blocks of a number and its divisibility.

In this article, we will learn what are factors of 10, how to find factors of 10, factor tree, and prime factorization of 10.

In mathematics, a factor refers to a number that can evenly divide another number without leaving a remainder.

What are Factors of 10?

The factors of 10 are the numbers that can divide 10 exactly, leaving no remainder behind. These numbers can be multiplied together to give a product equal to 10. The factors of 10 are mentioned below:

Factors of 10 are 1, 2, 5 and 10

10/1 = 10, remainder = 0,

10/2 = 5, remainder = 0,

10/5 = 2, remainder=0,

10/10 = 1, remainder = 0,

As shown in the above examples, if we divide the number by 10 and if we get its reminder as 0 then we say that it is the factor of 10. Like in this example 1, 2, 5, 10 are the factors of the 10.

All Factors of 10

Here is a list of all the factors of 10:

Factors of 10 are: 1, 2, 5, and 10

Learn, Factors

Prime Factors of 10

To find the prime factors of a number, you decompose it into a product of prime numbers.

10 = 2 × 5

Therefore, the prime factors of 10 are 2 and 5. Both 2 and 5 are prime numbers because they can only be divided evenly by 1 and themselves, making them indivisible by any other number.

How to Find Factors of 10?

We know that factors divide the given number evenly and factors when multiplied together to give the original number. Hence, we can find factors of 10 using following two methods

• Factors of 10 using Division Method
• Factors of 10 using Multiplication Method

Factors of 10 using Division Method

To find the factors of 10 using the division method, follow these steps:

1. Start with 1:
   • Begin with the number 1.
2. Division Check:
   • Check if 10 can be divided evenly by 1. Since it can, 1 is a factor.
3. Increase the Number
   • Move to the next number (2) and check if 10 is divisible by 2. If yes, 2 is a factor.
4. Continue the Above Steps
   • Repeat this process for subsequent numbers until you reach 10.
5. List the Factors:
   • Compile the list of numbers that divide 10 without a remainder. These are the factors.

Factors of 10 using Multiplication Method

To find the factors of 10 using the multiplication method, follow these steps:

1. Identify Pairs:
   • Look for pairs of numbers whose product is 10.
2. Start with 1:
   • Start with 1 and its product with 10.
3. Increase the Numbers:
   • Move to the next number (2) and find its product with another number until you cover all pairs.
4. List the Factors:
   • Compile the list of numbers obtained from the multiplication pairs. These are the factors.

These two methods provide different approaches to finding the factors of 10. You can choose the method that suits you best or use a combination of both for a comprehensive understanding.

Prime Factorization of 10

Prime factorization involves expressing a number as the product of its prime factors. Following are the steps to find the prime factorization of the any number:

1. Start with the Number:
   • Begin with the given number for which you want to find the prime factorization.
2. Find the Smallest Prime Factor:
   • Identify the smallest prime number that divides the given number without leaving a remainder. This is typically 2, as it’s the smallest prime number.
3. Divide and Repeat:
   • Divide the original number by the smallest prime factor found in step 2. If the result is a prime number, you have found the prime factorization. If not, repeat the process for the quotient.
4. Continue until Prime:
   • Continue the division process, using the smallest prime factor, until the result is a prime number. At this point, you have found the prime factorization.
5. Write the Prime Factors:
   • Write down all the prime numbers you obtained from the division.

For example, let’s find the prime factorization of 10:

• Start with 10.
• The smallest prime factor is 2. 10÷2=5
• 5 is a prime number, so the prime factorization of 10 is 2×5

So, the prime factorization of 10 is 2 × 5

Prime Factorization of 10

Factor Tree of 10

A factor tree is a graphical representation used to find the prime factorization of a number.

Below is the factor tree of the 10:

Factor Tree of 10

Factor Pairs of 10

Factor pairs are the pairs of numbers that multiply together to give a certain product. In the case of 10, the factor pairs are the combinations of two numbers that multiply to equal 10.

Positive Factor Pairs of 10

Positive factor pairs of 10 are the combinations of two positive integers that multiply to give the original number, which is 10. Here are the positive factor pairs of 10:

1 × 10 = 10

2 × 5 = 10

So, the positive factor pairs of 10 are (1, 10) and (2, 5). Each pair consists of positive integers, and when you multiply the numbers in each pair, you get the product 10.

Negative Factor Pairs of 10

Negative factor pairs of 10 are:

(-1) × (-10) = 10

(-2) × (-5) = 10

Each negative pair consists of two negative factors of 10 are (-1, -10) and (-2, -5)

Solved Examples on Factors of 10

Example 1: What is the sum of all the factors of 10?

Solution:

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

Sum of the factors of 10 = 1 + 2 + 5 + 10

Sum of the factors of 10 = 18

Example 2: If b is a factor of 10 and b > 1, What is the largest possible value of b?

Solution:

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

Largest factor of 10, other than 1 and 10, is 5.

Example 3: Find two factors of 10 whose product is equal to 10.

Solution:

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

Two factors of 10 whose product is 10 are:

2 and 5 (because 2 × 5 = 10)

Example 4: If d is a factor of both 10 and 6, what are the possible values of d?

Solution:

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

Factors of 6 are 1, 2, 3, and 6.

Common factors of 10 and 6 are 1 and 2.

Example 5: Express 10 as the product of its prime factors.

Solution:

10 expressed as the prime factorization of 10 is:

10 = 2×5

Factors of 10 – Practice Questions

Q1. Express 10 as the product of its prime factors.

Q2. If n is a factor of both 10 and 15, what are the possible values of n ?

Q3. Determine the number of positive factors of 10.

Q4. Find two pairs of different factors of 10 whose products are equal.

Q5. If p is a factor of 10 and p > 1, what is the smallest possible value of p ?

Q6. Express 10 as the sum of two of its factors.

Factors of 10 – Frequently Asked Questions

What are the Factors of 10?

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

How do you Find the Factors of 10?

To find the factors of 10, list the positive integers starting from 1 and check which ones divide 10 without leaving a remainder.

What is the Sum of Factors of 10?

The sum of the factors of 10 is 18 (1 + 2 + 5 + 10).

What is the Prime Factorization of 10?

The prime factorization of 10 is 2 × 5.

How many Factors does 10 have?

The number 10 has four factors: 1, 2, 5, and 10.

How to Express 10 as the Product of its Prime Factors?

10 can be expressed as product of prime factors as 10 = 2 × 5.

Are there Negative Factors of 10?

Conventionally, factors are considered as positive integers, but if considering negative factors in terms of multiplication, examples could be -1, -2, -5 and -10

Can 10 be Expressed as the Sum of Two of its Factors?

Yes, 10 can be expressed as the sum of 2 and 8, which are two of its factors (2 + 8 = 10).

Is 10 a Prime Number?

No 10 is not a Prime Number as it has more than 2 factors