1. Steps to find factors of 268 using Division Method

Example: Find factors of 268

  • Divide 268 by 1: 268 ÷ 1 : Remainder = 0
  • Divide 268 by 2: 268 ÷ 2 : Remainder = 0
  • Divide 268 by 4: 268 ÷ 4 : Remainder = 0
  • Divide 268 by 67: 268 ÷ 67 : Remainder = 0
  • Divide 268 by 134: 268 ÷ 134 : Remainder = 0
  • Divide 268 by 268: 268 ÷ 268 : Remainder = 0

Hence, Factors of 268 are 1, 2, 4, 67, 134, and 268

2. Steps to find factors of 268 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 268 using the division method, follow these steps:

  • Step 1. Start dividing 268 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 268, which is 2. Divide 268 by 2 to obtain the quotient (134).
    268 ÷ 2 = 134
  • Step 3. Repeat step 1 with the obtained quotient (134).
    134 ÷ 2 = 67
    67 ÷ 67 = 1

So, the prime factorization of 268 is, 268 = 2 x 2 x 67.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 268 as shown below:

So, the prime factorization of 268 is, 268 = 2 x 2 x 67.

3. Find factors of 268 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 268 would be the two numbers which, when multiplied, give 268 as the result.

The following table represents the calculation of factors of 268 in pairs:

Factor Pair Pair Factorization
1 and 268 1 x 268 = 268
2 and 134 2 x 134 = 268
4 and 67 4 x 67 = 268

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 268. They are called negative pair factors.

Hence, the negative pairs of 268 would be ( -1 , -268 ) , ( -2 , -134 ) and ( -4 , -67 ) .

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. 268 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 268.
  • Every number is a factor of zero (0), since 268 x 0 = 0.
  • 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, 4, 67, 134, 268 are exact divisors of 268.
  • Factors of 268 are 1, 2, 4, 67, 134, 268. Each factor divides 268 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 67, 134, 268 are all less than or equal to 268.

Frequently Asked Questions

  • Which is the smallest prime factor of 268?

    The smallest prime factor of 268 is 2.

  • Is 268 a whole number?

    Yes 268 is a whole number.

  • What are the prime factors of 268?

    The factors of 268 are 1, 2, 4, 67, 134, 268.
    Prime factors of 268 are 2, 2, 67.

  • What two numbers make 268?

    Two numbers that make 268 are 2 and 134.

  • What are multiples of 268?

    First five multiples of 268 are 536, 804, 1072, 1340.

  • What is the sum of all factors of 268?

    The sum of all factors of 268 is 476.

  • What are five multiples of 268?

    First five multiples of 268 are 536, 804, 1072, 1340, 1608.

  • Is 268 a perfect square?

    No 268 is not a perfect square.

  • What is the greatest prime factors of 268?

    The greatest prime factor of 268 is 67.

Examples of Factors

How many factors are there for 268?

Factors of 268 are 1, 2, 4, 67, 134, 268.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 268. Can you predict the answer?

5 factor(s) of 268 are 1, 2, 4, 67, 134.

Sammy is puzzled while calculating the prime factors of 268. Can you help him find them?

Factors of 268 are 1, 2, 4, 67, 134, 268.
Prime factors of 268 are 2, 2, 67

What is prime factorization of 268?

Prime factorization of 268 is 2 x 2 x 67 = 22 x 67.

Ariel has been assigned the task to find the product of all the prime factors of 268. Can you help her?

Prime factors of 268 are 2, 2, 67.
Hence, the product of prime factors of 134.

Can you help Rubel to find out the product of the even factors of 268?

Factors of 268 are 1, 2, 4, 67, 134, 268.
Even factors of 268 are 2, 4, 134, 268.
Hence, product of even factors of 268 is; 2 x 4 x 134 x 268 = 287296.

Joy wants to calculate mean of all the factors of 268. Help him in finding the mean of 268.

Factors of 268 are 1, 2, 4, 67, 134, 268.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 268 is 1 + 2 + 4 + 67 + 134 + 268 = 476.
Hence, the mean of factors of 268 is 476 ÷ 6 = 79.33.