Find Prime Factorization/Factors Of 10 - Cuemath

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Factors of 10 are the list of integers that we can split evenly into 10. There are overall 4 factors of 10 i.e. 1, 2, 5 and 10 where 10 is the biggest factor. The Prime Factors of 10 are 1, 2, 5, 10 and its Factors in Pairs are (1, 10) and (2, 5).

• Factors of 10: 1, 2, 5 and 10
• Negative Factors of 10: -1, -2, -5 and -10
• Prime Factors of 10: 2, 5
• Prime Factorization of 10: 2 × 5 = 2 × 5
• Sum of Factors of 10: 18

1.	What Are the Factors of 10?
2.	Important Notes
3.	How to Calculate Factors of 10?
4.	Factors of 10 by Prime Factorization
5.	Factors of 10 in Pairs
6.	FAQs on Factors of 10

What are the factors of 10?

The factors of 10 are the numbers that exactly divide 10.

You can observe that the numbers 1, 2, 5, and 10 on dividing 10 leaves the remainder as 0.

This means 1, 2, 5, and 10 exactly divide the number 10

They are the factors of 10

Important Notes

• Factors of a number are always less than or equal to the original number.
• The remainder obtained on dividing a number by its factor is always 0.
•  Every composite number can be uniquely expressed as the product of its prime factors.
• Prime numbers have only two factors.

How to Calculate the Factors of 10?

Let's find the pair of two numbers whose product is equal to 10

2 x 5 = 10

10 x 1 = 10

So, we have only these two pairs of numbers that give us the product 10

Factors of 10 are the numbers when multiplied together, give the product as 10

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

Factors of 10 by Prime Factorization

Prime factorization is a way of expressing a number as a product of its prime factors.

10 is a composite number.

So, it can be written as the product of prime numbers.

To find the prime factors, we will break down the number 10 into the set of primes which when multiplied together gives the result as 10.

 

The only prime numbers that exactly divide 10 are 2 and 5

Factors of 10 in Pairs

The pair of numbers which gives 10 when multiplied are known as factor pairs of 104

Following are the factors of 10 in pairs.

Product form of 10	Pair factor
1 x 10 = 10	(1,10)
2 x 5 = 10	(2,5)

Pairs of factors of 10 are: (1,10), (2,5).

Let's have a look at the negative pair factors of 10

So, if we consider negative integers, then both the numbers in the pair factors will be negative. 

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

So, we can have factor pairs of 10 as (-1,-10) ; (-2,-5).

 

Solved Examples

1. Example 1

   Mia and Rene are playing with circles.

   Rene writes the factors of 10 in the red circle and Mia writes the factors of 20 in the blue circle.

    

   

   Can you help them?

   Solution

   Factors of 10 are 1, 2, 5, and 10

   Factors of 20 are 1, 2, 4, 5, 10, and 20

   The common factors of 10 and 20 are 1, 2, 5, and 10

2. Example 2

   Aaron is asked to find the missing numbers in the factor trees of 18, 9, and 12

    

    

    

   Can you help him complete all the factor trees?

   Are there any common factors of 9 and 10? 

   Solution

   Let's find the missing factor in the factor tree of 18

   Pair 9 and 2 forms a factor pair of 18

   So, 9 is a missing factor of 18

   Now, let's find the missing factor in the factor tree of 12

   The missing number is a factor of 4 as well.

   Pair 2 and 2 forms a factor pair of 4

   So, 2 is a missing factor of 12

   Let's see the factors of 9 and 10

   Factors of 9: 1, 3, 9

   Factors of 10: 1, 2, 5, 10

   So, 1 is a common factor of 9 and 10

   Therefore, The missing factors of 18 and 12 are shown in the factor tree. The common factor of 9 and 10 is 1.

3. Example 3: How many factors are there for 10?

   Solution:

   The factors of 10 are 1, 2, 5, 10. Therefore, 10 has 4 factors.

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FAQs on Factors of 10

What are the Factors of 10?

The factors of 10 are 1, 2, 5, 10 and its negative factors are -1, -2, -5, -10.

What are the Prime Factors of 10?

The prime factors of 10 are 2, 5.

What is the Greatest Common Factor of 10 and 6?

The factors of 10 and 6 are 1, 2, 5, 10 and 1, 2, 3, 6 respectively. Common factors of 10 and 6 are [1, 2]. Hence, the Greatest Common Factor (GCF) of 10 and 6 is 2.

What is the Sum of all the Factors of 10?

Since all factors of 10 are 1, 2, 5, 10 therefore, the sum of its factors is 1 + 2 + 5 + 10 = 18.

How Many Factors of 10 are also common to the Factors of 6?

Since, the factors of 10 are 1, 2, 5, 10 and the factors of 6 are 1, 2, 3, 6. Hence, [1, 2] are the common factors of 10 and 6.

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