1. Steps to find factors of 529 using Division Method

Example: Find factors of 529

  • Divide 529 by 1: 529 ÷ 1 : Remainder = 0
  • Divide 529 by 23: 529 ÷ 23 : Remainder = 0
  • Divide 529 by 529: 529 ÷ 529 : Remainder = 0

Hence, Factors of 529 are 1, 23, and 529

2. Steps to find factors of 529 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 529 using the division method, follow these steps:

  • Step 1. Start dividing 529 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 529, which is 23. Divide 529 by 23 to obtain the quotient (23).
    529 ÷ 23 = 23
  • Step 3. Repeat step 1 with the obtained quotient (23).
    23 ÷ 23 = 1

So, the prime factorization of 529 is, 529 = 23 x 23.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 529 as shown below:

So, the prime factorization of 529 is, 529 = 23 x 23.

3. Find factors of 529 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 529 would be the two numbers which, when multiplied, give 529 as the result.

The following table represents the calculation of factors of 529 in pairs:

Factor Pair Pair Factorization
1 and 529 1 x 529 = 529
23 and 23 23 x 23 = 529

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 529. They are called negative pair factors.

Hence, the negative pairs of 529 would be ( -1 , -529 ) , ( -23 , -23 ) .

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, 23, 529 are exact divisors of 529.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 529 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 529.

Frequently Asked Questions

  • Which is the smallest prime factor of 529?

    The smallest prime factor of 529 is 23.

  • Is 529 a whole number?

    Yes 529 is a whole number.

  • What are the prime factors of 529?

    The factors of 529 are 1, 23, 529.
    Prime factors of 529 are 23, 23.

  • What two numbers make 529?

    Two numbers that make 529 are 23 and 23.

  • What are multiples of 529?

    First five multiples of 529 are 1058, 1587, 2116, 2645.

  • What is the sum of all factors of 529?

    The sum of all factors of 529 is 553.

  • What are five multiples of 529?

    First five multiples of 529 are 1058, 1587, 2116, 2645, 3174.

  • Is 529 a perfect square?

    Yes 529 is a perfect square.

  • What is the greatest prime factors of 529?

    The greatest prime factor of 529 is 23.

Examples of Factors

How many factors are there for 529?

Factors of 529 are 1, 23, 529.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 529. Can you predict the answer?

2 factor(s) of 529 are 1, 23.

Sammy is puzzled while calculating the prime factors of 529. Can you help him find them?

Factors of 529 are 1, 23, 529.
Prime factors of 529 are 23, 23

What is prime factorization of 529?

Prime factorization of 529 is 23 x 23 = 232.

Ariel has been assigned the task to find the product of all the prime factors of 529. Can you help her?

Prime factors of 529 are 23, 23.
Hence, the product of prime factors of 23.

Can you help Rubel to find out the product of the even factors of 529?

Factors of 529 are 1, 23, 529.
Even factors of 529 are 0.
Hence, product of even factors of 529 is; 0 = 0.

Joy wants to calculate mean of all the factors of 529. Help him in finding the mean of 529.

Factors of 529 are 1, 23, 529.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 529 is 1 + 23 + 529 = 553.
Hence, the mean of factors of 529 is 553 ÷ 3 = 184.33.