Factors of 338

The factors of 338 are the numbers that divide 338 evenly.

Positive Factors: These are the positive numbers that divide 338 evenly. 
Positive factors are 1, 2, 13, 26, 169, and 338.

Negative Factors: These are negative counterparts of the positive factors.
Negative factors are -1, -2, -13, -26, -169, -338

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 338 as the product.

Prime factors: 2, 13

Prime Factorization: Prime factorization involves breaking 338 into its prime factors.
It is expressed as 2¹×13²

Table listing the factors of 338

This breakdown helps in understanding the various factors of 338, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 338.

Methods to find the factors of 338:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

The multiplication method finds the pair of factors that give 338 as their product.

Step 1: Find the pair of numbers whose product is 338.

Step 2: The factors are those numbers, when multiplied, give 338.

Step 3: Make a list of numbers whose product will be 338.

A list of numbers whose products are 338 is given below:

• 1 × 338 = 338
• 2 × 169 = 338
• 13 × 26 = 338

Thus, the factors of 338 are 1, 2, 13, 26, 169, and 338.

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.

Example: 338÷1=338

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 338 are 1, 2, 13, 26, 169, and 338.
 

Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using its factors and expressed in the form of prime factors, is the prime factorization of a number.

Prime Factors of 338: Number 338 has two prime factors.

Prime factors of 338: 2, 13

Steps to Find the Prime Factors of 338:

Divide 338 by the smallest prime number 2:

• 338 ÷ 2 = 169

Divide 169 by the next prime number 13:

• 169 ÷ 13 = 13 

Divide 13 by itself:

• 13 ÷ 13 = 1

Prime Factorization of 338:

Expressed as 2¹×13²
 

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

This tree shows the breakdown of 338 into its prime factors: 2 × 13 × 13.

Positive and Negative Factor Pairs of 338

Factors of 338 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs: (1, 338), (2, 169), (13, 26)

Negative Factor Pairs: (-1, -338), (-2, -169), (-13, -26)

• Factor: A number that divides another number completely without leaving a remainder.  

• Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.

• Negative Factor: The negative counterparts of positive factors. For example, the negative factors of 338 are -1, -2, -13, -26, -169, and -338.

• Factor Tree: A visual representation that breaks down a number into its prime factors step by step, resembling the branches of a tree.

• Multiplication Method: A method of finding factors by identifying pairs of numbers whose product equals the given number.