1. Steps to find factors of 2704 using Division Method

Example: Find factors of 2704

  • Divide 2704 by 1: 2704 ÷ 1 : Remainder = 0
  • Divide 2704 by 2: 2704 ÷ 2 : Remainder = 0
  • Divide 2704 by 4: 2704 ÷ 4 : Remainder = 0
  • Divide 2704 by 8: 2704 ÷ 8 : Remainder = 0
  • Divide 2704 by 13: 2704 ÷ 13 : Remainder = 0
  • Divide 2704 by 16: 2704 ÷ 16 : Remainder = 0
  • Divide 2704 by 26: 2704 ÷ 26 : Remainder = 0
  • Divide 2704 by 52: 2704 ÷ 52 : Remainder = 0
  • Divide 2704 by 104: 2704 ÷ 104 : Remainder = 0
  • Divide 2704 by 169: 2704 ÷ 169 : Remainder = 0
  • Divide 2704 by 208: 2704 ÷ 208 : Remainder = 0
  • Divide 2704 by 338: 2704 ÷ 338 : Remainder = 0
  • Divide 2704 by 676: 2704 ÷ 676 : Remainder = 0
  • Divide 2704 by 1352: 2704 ÷ 1352 : Remainder = 0
  • Divide 2704 by 2704: 2704 ÷ 2704 : Remainder = 0

Hence, Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, and 2704

2. Steps to find factors of 2704 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 2704 using the division method, follow these steps:

  • Step 1. Start dividing 2704 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 2704, which is 2. Divide 2704 by 2 to obtain the quotient (1352).
    2704 ÷ 2 = 1352
  • Step 3. Repeat step 1 with the obtained quotient (1352).
    1352 ÷ 2 = 676
    676 ÷ 2 = 338
    338 ÷ 2 = 169
    169 ÷ 13 = 13
    13 ÷ 13 = 1

So, the prime factorization of 2704 is, 2704 = 2 x 2 x 2 x 2 x 13 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2704 as shown below:

So, the prime factorization of 2704 is, 2704 = 2 x 2 x 2 x 2 x 13 x 13.

3. Find factors of 2704 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 2704 would be the two numbers which, when multiplied, give 2704 as the result.

The following table represents the calculation of factors of 2704 in pairs:

Factor Pair Pair Factorization
1 and 2704 1 x 2704 = 2704
2 and 1352 2 x 1352 = 2704
4 and 676 4 x 676 = 2704
8 and 338 8 x 338 = 2704
13 and 208 13 x 208 = 2704
16 and 169 16 x 169 = 2704
26 and 104 26 x 104 = 2704
52 and 52 52 x 52 = 2704

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 2704. They are called negative pair factors.

Hence, the negative pairs of 2704 would be ( -1 , -2704 ) , ( -2 , -1352 ) , ( -4 , -676 ) , ( -8 , -338 ) , ( -13 , -208 ) , ( -16 , -169 ) , ( -26 , -104 ) and ( -52 , -52 ) .

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. 2704 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2704.
  • Every number is a factor of zero (0), since 2704 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, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 are exact divisors of 2704.
  • Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704. Each factor divides 2704 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 are all less than or equal to 2704.

Frequently Asked Questions

  • Is 2704 a perfect square?

    Yes 2704 is a perfect square.

  • What are factors of 2704?

    Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.

  • Which is greatest factor of 2704?

    The greatest factor of 2704 is 1352.

  • What is the sum of all factors of 2704?

    The sum of all factors of 2704 is 5673.

  • What are multiples of 2704?

    First five multiples of 2704 are 5408, 8112, 10816, 13520.

  • What is the greatest prime factors of 2704?

    The greatest prime factor of 2704 is 13.

  • What are six multiples of 2704?

    First five multiples of 2704 are 5408, 8112, 10816, 13520, 16224, 18928.

  • What is prime factorization of 2704?

    Prime factorization of 2704 is 2 x 2 x 2 x 2 x 13 x 13.

  • Is 2704 a whole number?

    Yes 2704 is a whole number.

Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2704? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.
Negative factors are -1, -2, -4, -8, -13, -16, -26, -52, -104, -169, -208, -338, -676, -1352, -2704.

Can you help Sammy find out the product of the odd factors of 2704?

Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.
Odd factors of 2704 are 1, 13, 169.
Hence product of odd factors of 2704 is; 1 x 13 x 169 = 2197.

Joey wants to write all the prime factors of 2704 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2704 are 2, 2, 2, 2, 13, 13.
So in exponential form it can be written as 24 x 132.

How many factors are there for 2704?

Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.
So there are in total 15 factors.

Kevin has been asked to write 14 factor(s) of 2704. Can you predict the answer?

14 factor(s) of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352.

Sammy is puzzled while calculating the prime factors of 2704. Can you help him find them?

Factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.
Prime factors of 2704 are 2, 2, 2, 2, 13, 13

What is prime factorization of 2704?

Prime factorization of 2704 is 2 x 2 x 2 x 2 x 13 x 13 = 24 x 132.