Factors of 59

The factors of 59 are the numbers that divide 59 exactly without leaving any remainder. In other words, the numbers that are multiplied together resulting in the number 59 are the factors of 59. The factors of 59 and its pair factors can be expressed in positive and negative form, but they cannot be represented in the fraction or decimal form. In this article, we will learn the factors of 59, positive and negative pair factors of 59, how to find the prime factors of 59 using the prime factorization method, and many solved examples.

Table of Contents:

• What are the Factors of 59?
• Pair Factors of 59
• Factors of 59 by Division Method
• Prime Factorization of 59
• Solved Examples
• FAQs

What are the Factors of 59?

In Mathematics, the factors of a number are the numbers that divide the given number evenly without leaving a remainder value. Thus, the factors of 59 are the numbers that are multiplied in pairs resulting in the original number 59. As 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59. Similarly, the negative factors of 59 are -1 and -59.

Pair Factors of 59

As discussed above, the pair factor of 59 is expressed in both positive and negative form. A pair of numbers that are multiplied together, and it results in 59 are the pair factors of 59. Since the number 59 is a prime number, it has only one positive pair factor and one negative pair factor. The following are the positive and negative pair factors of 59.

Positive Pair Factor of 59:

Negative Pair Factor of 59:

Therefore, the positive and negative pair factors of 59 are (1, 59) and (-1, -59), respectively.

Factors of 59 by Division Method

The factors of 59 using the division method are found by dividing the number 59 by different integers. If the integers exactly divide the number 59, then those integers are the factors of 59. The factors of 59 using the division method are found as follows:

• 59/1 = 59 (Factor is 1 and Remainder is 0)
• 59/59 =1 (Factor is 59 and Remainder is 0)

If any numbers other than 1 and 59 divides 59, it leaves a remainder value. Hence, the factors of 59 are 1 and 59.

Prime Factorization of 59

In the prime factorization of 59, the number 59 is written in the form of the product of its prime factors. Thus, the process of finding prime factors of 59 using the prime factorization method is given as follows:

Take a pair factor of 59, say (1, 59)

Now, check the factors of 59, whether it is prime or composite. If a number is a prime number, leave the number as it is. If a number is a composite number, split the number into its prime factors.

Here, the factors of 59, such as 1 and 59, are prime numbers.

Thus, 59 is written as the product of 1 and 59.

Therefore, the prime factorization of 59 is 1 × 59 or 59.

Video Lesson on Prime Factors

Solved Examples

Example 1:

What are the common factors of 59 and 58?

Solution:

The factors of 59 are 1 and 59.

The factors of 58 are 1, 2, 29 and 58.

Thus, the common factor of 59 and 58 is 1.

Example 2:

Find the common factors of 59 and 60.

Solution:

Factors of 59 = 1 and 59.

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Hence, the common factor of 59 and 60 is 1.

Example 3:

Find the common factors of 59 and 53.

Solution:

The factors of 59 are 1 and 59.

The factors of 53 are 1 and 53.

As both the numbers are prime numbers, the common factor of 59 and 53 is 1.

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