Find Prime Factorization/Factors Of 13 - Cuemath

Factors of 13

Factors of 13 are the list of integers that we can split evenly into 13. There are overall 2 factors of 13 among which 13 is the biggest factor and its positive factors are 1 and 13. The Prime Factor of 13 is 1, 13 and its Factors in Pairs are (1, 13).

• Factors of 13: 1 and 13
• Negative Factors of 13: -1 and -13
• Prime Factors of 13: 13
• Prime Factorization of 13: 13
• Sum of Factors of 13: 14

1.	What Are the Factors of 13?
2.	How to Calculate the Factors of 13?
3.	Important Notes
4.	Factors of 13 by Prime Factorization
5.	Factors of 13 in Pairs
6.	FAQs on Factors of 13

What Are the Factors of 13?

The factor of a number is that number that divides it completely while leaving no remainder. 

For example, to find the factors of the number 13, we will have to perform division on 13 and find the numbers which divide 13 completely, leaving no remainders.

Since it is a prime number, it will have only two factors 1 and 13.

The below figure provides the representation of the above definition.

Explore factors using illustrations and interactive examples

• Factors of 12 - Factors of 12 are 1, 2, 3, 4, 6, and 12. 
• Factors of 14 - Factors of 14 are 1, 2, 7, and 14.
• Factors of 130 - The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130.
• Factors of 132 - The factors of 147 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.

How to Calculate the Factors of 13? 

To calculate the factors of any number, in this case, 13, we need to find all the numbers that would divide 13 without leaving any remainder.

We start with the number 1, then check for numbers 2, 3, 4, 5, etc. up to 7 (approximate half of 13).

The number 1 and the number itself are always a factor of the given number.

Refer to the following table to check the division of 13 with its factors: 

Division	Factor
13/1 = 13	Remainder = 0 Factor = 1
13/13 = 1	Remainder = 0 Factor = 13

Important Notes

• 13 has only two factors, 1 and 13. Hence, it is a prime number.
• 13 is not a perfect square. 169 is the square of 13.
• The smallest multiple and largest factor of 13 is 13.

Factors of 13 Using Prime Factorization

Prime factorization of a number refers to breaking down a number into the product of its prime factors.

Different methods can be used to find the prime factorization of a number and to find its prime factors.

Method 1 - Division Method

To find the prime factors of 13 using the division method, we will do the following.

Step 1: Start dividing 13 from the smallest prime number i.e., 2, 3, 5, and so on, and find the smallest prime factor of the number.

Step 2: After finding the smallest prime factor of the number 13, that is 13 itself, divide 13 by 13 to obtain the quotient as 1.

13 ÷ 13 = 1

Thus, the prime factorization of 13 is 13 × 1.

Method 2 - Factor Tree Method

We can do the same procedure using the factor tree for 13 as shown in the figure given below:

Thus, the prime factorization of 13 is 13 x 1.

Factors of 13 in Pairs

Pair factors are the factors of a number given in pairs which when multiplied together give the original number.

The pair factors of 13 would be the two numbers which when multiplied together result in the value 13.

The following table shows the pair factors of 13. 

Factor Pair	Pair Factorization
1 and 13	1 x 13 = 13

 

Solved Examples

1. Example 1 Can you help Jess calculate the sum of all the factors of 13?

   Solution

   We know, the factors of 13 = 1 and 13

   Thus, the sum of all the factors = 1 + 13 = 14

2. Example 2 Nora is finding the factors of numbers. She wants to find the common factors of 13 and 52. Can you help her find them?

   Solution

   We know, the factors of 13 = 1 and 13

   Factors of 52 = 1, 2, 4, 13, 26, and 52

   Thus, the common factors of 13 and 52 are 1 and 13.

3. Example 3: Find the product of all the prime factors of 13.

   Solution:

   Since the prime factors of 13 are 13. Therefore, the product of prime factors = 13 = 13.

Show Solution >

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FAQs on Factors of 13

What are the Factors of 13?

The factors of 13 are 1, 13 and its negative factors are -1, -13.

What numbers are the Pair Factors of 13?

The pair factors of 13 are (1, 13).

What is the Sum of all the Factors of 13?

Factors of 13 are 1, 13 and, the sum of all these factors is 1 + 13 = 14

What is the Greatest Common Factor of 13 and 3?

The factors of 13 are 1, 13 and the factors of 3 are 1, 3. 13 and 3 have only one common factor which is 1. This implies that 13 and 3 are co-prime. Hence, the Greatest Common Factor (GCF) of 13 and 3 is 1.

How Many Factors of 13 are also common to the Factors of 8?

Since the factors of 13 are 1, 13, and factors of 8 are 1, 2, 4, 8. Hence, 13 and 8 have only one common factor which is 1. Therefore, 13 and 8 are co-prime.