Factors of 529

The factors of 529 are the list of numbers that divide 529 evenly without leaving any remainder value. The factors and the pair factors of 529 can be represented in both positive and negative form, but they cannot be in decimal or fractional form. For example, the pair factor of 529 is represented as (1, 529) or (-1, -529). If we multiply a pair of negative numbers, such as multiplying -1 and -529, it will result in the number 529. Here, we are going to discuss what are the factors of 529, positive and negative pair factors of 529, prime factorization of 529 and many solved examples.

Table of Contents:

• What are the Factors of 529?
• Pair Factors of 529
• Factors of 529 by Division Method
• Prime Factorization of 529
• Solved Examples
• FAQs

What are the Factors of 529?

In Mathematics, if a given number is completely divisible by the integer numbers, then the integers are the factors of 529. In other words, the factors of 529 are the numbers that are multiplied in pairs resulting in the original number 529. Since the number 529 is a composite number, it has more than two factors. Therefore, the factors of 529 are 1, 23 and 529. Likewise, the negative factors of 529 are -1, -23 and -529.

Pair Factors of 529

As the number 529 is a composite number, it has more than one pair factor. As discussed above, the pair factors of 529 are represented in both positive and negative form. The following are the positive and negative pair factors of 529.

Positive Pair Factors of 529:

Therefore, the positive pair factors of 529 are (1, 529) and (23, 23).

Negative Pair Factors of 529:

Therefore, the negative pair factors of 529 are (-1, -529) and (-23, -23)

Note: If (x, y) is a factor of a number, then (y, x) is also a factor of a number. For example, if (1, 529) is a pair factor of a number, then (529, 1) is also a pair factor of 529. Similarly, (-1, -529) is a negative pair factor of 529, then (-529, -1) is also considered as a negative pair factor of 529.

Factors of 529 by Division Method

The factors of 529 are found using the division method. In the division method, the factors of 529 are determined by dividing 529 by different integers. If the integers divide 529 completely and leave a remainder value of 0, then the integers are the factors of 529. Now, let us discuss how to find the factors of 529 using the division method.

• 529/1 = 529 (Factor is 1 and Remainder is 0)
• 529/23 = 23 (Factor is 23 and Remainder is 0)
• 529/529 = 1 (Factor is 529 and Remainder is 0)

Hence, the factors of 529 are 1, 23 and 529.

Note: If we divide 529 by any numbers other than 1, 23 and 529, it leaves a remainder of some integer value.

Prime Factorization of 529

The prime factorization of 529 is the process of writing the number 529 as the product of its prime factors. Go through the following procedure to find the prime factors of 529 using the prime factorization method.

Consider a pair factor of 529, say (1, 529)

Here, ignore the number 1 as it is neither prime nor composite. Now, take the other number 529, which is a composite number and it can be split further into its prime factors.

Thus, the number 529 is written as the product of 23 and 23, where 23 is a prime number. Thus, the prime factor of the number 529 is 23.

Therefore, the prime factorization of 529 is 23 × 23 or 23².

Note: The total number of factors of 529 can be found using the prime factorization of 529. Adding the number 1 to the exponent value, and multiplying it with the exponent of other existing factors results in the total number of factors of a number. We know that the prime factorization of 529 is 23² (i.e) (2+1) = 3. Therefore, the number 529 has 3 factors.

Video Lesson on Prime Factors

Solved Examples

Example 1:

What are the common factors of 529 and 527?

Solution:

The factors of 529 are 1, 23 and 529.

The factors of 527 are 1, 17, 31 and 527.

Thus, the common factor of 529 and 527 is 1.

Example 2:

Find the common factors of 529 and 23.

Solution:

Factors of 529 = 1, 23 and 529.

Factors of 23 = 1 and 23.

Therefore, the common factors of 529 and 23 are 1 and 23.

Example 3:

Find the common factors of 529 and 525.

Solution:

The factors of 529 are 1, 23 and 529.

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 and 525.

Thus, the common factor of 529 and 525 is 1.

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