1. Steps to find factors of 1729 using Division Method

Example: Find factors of 1729

  • Divide 1729 by 1: 1729 ÷ 1 : Remainder = 0
  • Divide 1729 by 7: 1729 ÷ 7 : Remainder = 0
  • Divide 1729 by 13: 1729 ÷ 13 : Remainder = 0
  • Divide 1729 by 19: 1729 ÷ 19 : Remainder = 0
  • Divide 1729 by 91: 1729 ÷ 91 : Remainder = 0
  • Divide 1729 by 133: 1729 ÷ 133 : Remainder = 0
  • Divide 1729 by 247: 1729 ÷ 247 : Remainder = 0
  • Divide 1729 by 1729: 1729 ÷ 1729 : Remainder = 0

Hence, Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, and 1729

2. Steps to find factors of 1729 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 1729 using the division method, follow these steps:

  • Step 1. Start dividing 1729 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 1729, which is 7. Divide 1729 by 7 to obtain the quotient (247).
    1729 ÷ 7 = 247
  • Step 3. Repeat step 1 with the obtained quotient (247).
    247 ÷ 13 = 19
    19 ÷ 19 = 1

So, the prime factorization of 1729 is, 1729 = 7 x 13 x 19.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1729 as shown below:

So, the prime factorization of 1729 is, 1729 = 7 x 13 x 19.

3. Find factors of 1729 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 1729 would be the two numbers which, when multiplied, give 1729 as the result.

The following table represents the calculation of factors of 1729 in pairs:

Factor Pair Pair Factorization
1 and 1729 1 x 1729 = 1729
7 and 247 7 x 247 = 1729
13 and 133 13 x 133 = 1729
19 and 91 19 x 91 = 1729

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 1729. They are called negative pair factors.

Hence, the negative pairs of 1729 would be ( -1 , -1729 ) , ( -7 , -247 ) , ( -13 , -133 ) and ( -19 , -91 ) .

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

  • Every factor of a number is an exact divisor of that number, example 1, 7, 13, 19, 91, 133, 247, 1729 are exact divisors of 1729.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 1729 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1729.

Frequently Asked Questions

  • What are the prime factors of 1729?

    The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.
    Prime factors of 1729 are 7, 13, 19.

  • What is the sum of all factors of 1729?

    The sum of all factors of 1729 is 2240.

  • What are the pair factors of 1729?

    Pair factors of 1729 are (1,1729), (7,247), (13,133), (19,91).

  • What two numbers make 1729?

    Two numbers that make 1729 are 7 and 247.

  • What are multiples of 1729?

    First five multiples of 1729 are 3458, 5187, 6916, 8645.

  • Is 1729 a perfect square?

    No 1729 is not a perfect square.

  • Which is greatest factor of 1729?

    The greatest factor of 1729 is 247.

  • How do you factors of 1729?

    Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.

  • What are five multiples of 1729?

    First five multiples of 1729 are 3458, 5187, 6916, 8645, 10374.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 1729?

Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.
Even factors of 1729 are 0.
Hence, product of even factors of 1729 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1729? Help her in writing all the factors.

Positive factors are 1, 7, 13, 19, 91, 133, 247, 1729.
Negative factors are -1, -7, -13, -19, -91, -133, -247, -1729.

How many factors are there for 1729?

Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 1729. Can you help him find them?

Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.
Prime factors of 1729 are 7, 13, 19

Joey wants to write all the prime factors of 1729 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1729 are 7, 13, 19.
So in exponential form it can be written as 7 x 13 x 19.

What is prime factorization of 1729?

Prime factorization of 1729 is 7 x 13 x 19 = 7 x 13 x 19.

Can you help Rubel to find out the product of the even factors of 1729?

Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729.
Even factors of 1729 are 0.
Hence, product of even factors of 1729 is; 0 = 0.