1. Steps to find factors of 338 using Division Method

Example: Find factors of 338

  • Divide 338 by 1: 338 ÷ 1 : Remainder = 0
  • Divide 338 by 2: 338 ÷ 2 : Remainder = 0
  • Divide 338 by 13: 338 ÷ 13 : Remainder = 0
  • Divide 338 by 26: 338 ÷ 26 : Remainder = 0
  • Divide 338 by 169: 338 ÷ 169 : Remainder = 0
  • Divide 338 by 338: 338 ÷ 338 : Remainder = 0

Hence, Factors of 338 are 1, 2, 13, 26, 169, and 338

2. Steps to find factors of 338 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 338 using the division method, follow these steps:

  • Step 1. Start dividing 338 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 338, which is 2. Divide 338 by 2 to obtain the quotient (169).
    338 ÷ 2 = 169
  • Step 3. Repeat step 1 with the obtained quotient (169).
    169 ÷ 13 = 13
    13 ÷ 13 = 1

So, the prime factorization of 338 is, 338 = 2 x 13 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 338 as shown below:

So, the prime factorization of 338 is, 338 = 2 x 13 x 13.

3. Find factors of 338 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 338 would be the two numbers which, when multiplied, give 338 as the result.

The following table represents the calculation of factors of 338 in pairs:

Factor Pair Pair Factorization
1 and 338 1 x 338 = 338
2 and 169 2 x 169 = 338
13 and 26 13 x 26 = 338

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 338. They are called negative pair factors.

Hence, the negative pairs of 338 would be ( -1 , -338 ) , ( -2 , -169 ) and ( -13 , -26 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 338 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 13, 26, 169, 338 are exact divisors of 338.
  • 1 is a factor of every number. Eg. 1 is a factor of 338.
  • Every number is a factor of zero (0), since 338 x 0 = 0.

Frequently Asked Questions

  • What are the pair factors of 338?

    Pair factors of 338 are (1,338), (2,169), (13,26).

  • What are five multiples of 338?

    First five multiples of 338 are 676, 1014, 1352, 1690, 2028.

  • What two numbers make 338?

    Two numbers that make 338 are 2 and 169.

  • What is the sum of all factors of 338?

    The sum of all factors of 338 is 549.

  • What are factors of -338?

    Factors of -338 are -1, -2, -13, -26, -169, -338.

  • What are factors of 338?

    Factors of 338 are 1, 2, 13, 26, 169, 338.

  • Is 338 a perfect square?

    No 338 is not a perfect square.

  • Which is the smallest prime factor of 338?

    Smallest prime factor of 338 is 2.

  • Which is greatest factor of 338?

    The greatest factor of 338 is 169.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 338?

Factors of 338 are 1, 2, 13, 26, 169, 338.
Odd factors of 338 are 1, 13, 169.
Hence product of odd factors of 338 is; 1 x 13 x 169 = 2197.

Joey wants to write all the prime factors of 338 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 338 are 2, 13, 13.
So in exponential form it can be written as 2 x 132.

How many factors are there for 338?

Factors of 338 are 1, 2, 13, 26, 169, 338.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 338. Can you predict the answer?

5 factor(s) of 338 are 1, 2, 13, 26, 169.

Sammy is puzzled while calculating the prime factors of 338. Can you help him find them?

Factors of 338 are 1, 2, 13, 26, 169, 338.
Prime factors of 338 are 2, 13, 13

What is prime factorization of 338?

Prime factorization of 338 is 2 x 13 x 13 = 2 x 132.

Can you help Rubel to find out the product of the even factors of 338?

Factors of 338 are 1, 2, 13, 26, 169, 338.
Even factors of 338 are 2, 26, 338.
Hence, product of even factors of 338 is; 2 x 26 x 338 = 17576.