Factors of 221

The factors of 221 are the numbers that divide 221 evenly without leaving any remainder. The factors and the pair factors of 221 can be represented in both positive and negative form, but the factors of 221 cannot be a decimal number or a fractional number. For example, the pair factors of 221 can be (1, 221) or (-1, -221). The multiplication of negative factors, such as multiplying -1 and -221, will result in the original number 221. In this article, we are going to learn the factors of 221, pair factors of 221, and how to find the prime factors of 221 using the prime factorization method.

Table of Contents:

• What are the Factors of 221?
• Pair Factors of 221
• Factors of 221 by Division Method
• Prime Factorization of 221
• Solved Examples
• FAQs

What are the Factors of 221?

The numbers that are multiplied together in pairs, resulting in the original number 221 are the factors of 221. In other words, the factors of 221 are the numbers that divide 221 completely and leave a remainder 0. As 221 is a composite number, it has more than two factors. Therefore, the factors of 221 are 1, 13, 17 and 221. Similarly, the negative factors of 221 are -1, -13, -17 and -221.

Pair Factors of 221

A pair of numbers that are multiplied together and results in 221 is called the pair factor of 221. As the number 221 has 4 factors, it should have 2 pair factors. The following are the positive and negative pair factors of 221.

Positive Pair Factors of 221:

Therefore, the positive pair factors of 221 are (1, 221) and (13, 17)

Negative Pair Factors of 221:

Thus, the negative pair factors of 221 are (-1, -221) and (-13, -17).

Factors of 221 by Division Method

In the division method, the factors of 221 can be easily found by dividing 221 by different integers. If the integer numbers divide 221 completely without leaving any remainder value, then the integers are the factors of 221. Now, let us start dividing the number 221 by 1 and then continue with the different numbers.

• 221/1 = 221 (Factor = 1 and Remainder = 0)
• 221/13 =17 (Factor = 13 and Remainder = 0)
• 221/17 = 13 (Factor = 17 and Remainder = 0)
• 221/221 = 1 (Factor = 221 and Remainder = 0)

Thus, the factors of 221 are 1, 13, 17 and 221.

Note: If we divide the number 221 by any numbers other than 1, 13, 17 and 221, it leaves a remainder of some value.

Prime Factorization of 221

The process of writing the number 221 as the product of its prime factors is called the prime factorization of 221. Go through the following procedure to find the prime factors of 221 using the prime factorization method.

Consider a pair factor of 221, say (1, 221). Now, check whether the numbers in the pair factors are prime or composite. If a number is a prime number, then leave the number as given. If a number is a composite number, split the composite number into its prime factors. We know that 1 is neither prime nor composite, and hence leave the number 1 as it is.

Now, take the other number 221, which is a composite number. It can be further split as the product of 13 and 17, where 13 and 17 are prime numbers.

Hence, write the number 221 as the product of 13 and 17.

Therefore, the prime factorization of 221 is 13 × 17.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 221 and 220.

Solution:

The factors of 221 are 1, 13, 17 and 221.

The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and 220.

Thus, the common factor of 221 and 220 is 1.

Example 2:

What are the common factors of 221 and 219?

Solution:

Factors of 221 = 1, 13, 17 and 221.

Factors of 219 = 1, 3, 73, 219.

Hence, the common factor of 221 and 219 is 1.

Example 3:

Find the common factors of 221 and 223.

Solution:

The factors of 221 are 1, 13, 17 and 221.

The factors of 223 are 1 and 223.

As the number 223 is a prime number, the common factor of 221 and 223 is 1.

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