1. Steps to find factors of 274 using Division Method

Example: Find factors of 274

  • Divide 274 by 1: 274 ÷ 1 : Remainder = 0
  • Divide 274 by 2: 274 ÷ 2 : Remainder = 0
  • Divide 274 by 137: 274 ÷ 137 : Remainder = 0
  • Divide 274 by 274: 274 ÷ 274 : Remainder = 0

Hence, Factors of 274 are 1, 2, 137, and 274

2. Steps to find factors of 274 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 274 using the division method, follow these steps:

  • Step 1. Start dividing 274 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 274, which is 2. Divide 274 by 2 to obtain the quotient (137).
    274 ÷ 2 = 137
  • Step 3. Repeat step 1 with the obtained quotient (137).
    137 ÷ 137 = 1

So, the prime factorization of 274 is, 274 = 2 x 137.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 274 as shown below:

So, the prime factorization of 274 is, 274 = 2 x 137.

3. Find factors of 274 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 274 would be the two numbers which, when multiplied, give 274 as the result.

The following table represents the calculation of factors of 274 in pairs:

Factor Pair Pair Factorization
1 and 274 1 x 274 = 274
2 and 137 2 x 137 = 274

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 274. They are called negative pair factors.

Hence, the negative pairs of 274 would be ( -1 , -274 ) , ( -2 , -137 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 274 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, 137, 274 are exact divisors of 274.
  • 1 is a factor of every number. Eg. 1 is a factor of 274.
  • Every number is a factor of zero (0), since 274 x 0 = 0.

Frequently Asked Questions

  • Is 274 a perfect square?

    No 274 is not a perfect square.

  • What are factors of 274?

    Factors of 274 are 1, 2, 137, 274.

  • Which is greatest factor of 274?

    The greatest factor of 274 is 137.

  • What is the sum of all factors of 274?

    The sum of all factors of 274 is 414.

  • What are multiples of 274?

    First five multiples of 274 are 548, 822, 1096, 1370.

  • What is the greatest prime factors of 274?

    The greatest prime factor of 274 is 137.

  • What are six multiples of 274?

    First five multiples of 274 are 548, 822, 1096, 1370, 1644, 1918.

  • What is prime factorization of 274?

    Prime factorization of 274 is 2 x 137.

  • Is 274 a whole number?

    Yes 274 is a whole number.

Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 274? Help her in writing all the factors.

Positive factors are 1, 2, 137, 274.
Negative factors are -1, -2, -137, -274.

Can you help Sammy find out the product of the odd factors of 274?

Factors of 274 are 1, 2, 137, 274.
Odd factors of 274 are 1, 137.
Hence product of odd factors of 274 is; 1 x 137 = 137.

Joey wants to write all the prime factors of 274 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 274 are 2, 137.
So in exponential form it can be written as 2 x 137.

How many factors are there for 274?

Factors of 274 are 1, 2, 137, 274.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 274. Can you predict the answer?

3 factor(s) of 274 are 1, 2, 137.

Sammy is puzzled while calculating the prime factors of 274. Can you help him find them?

Factors of 274 are 1, 2, 137, 274.
Prime factors of 274 are 2, 137

What is prime factorization of 274?

Prime factorization of 274 is 2 x 137 = 2 x 137.