Factors of 22

Factors of 22 are the list of integers that can be evenly divided into 22. There are overall 4 factors of 22 i.e. 1, 2, 11 and 22 where 22 is the biggest factor. The Prime Factors of 22 are 1, 2, 11, 22 and its Factors in Pairs are (1, 22) and (2, 11).

• Factors of 22: 1, 2, 11 and 22
• Negative Factors of 22: -1, -2, -11 and -22
• Prime Factors of 22: 2, 11
• Prime Factorization of 22: 2 × 11 = 2 × 11
• Sum of Factors of 22: 36

What are the Factors of 22?

The factor of a number is that number which divides it completely i.e., leaving no remainder. For example: For determing the factors of the number 22, we will have to perform division on 22 and find the numbers which divide 22 completely, leaving no remainders. The below diagram provides the representation of the above definition:

How to Calculate the Factors of 22?

To calculate the factors of any number, here in this case 22, we need to find all the numbers that would divide 22 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, etc. up to 11 (half of 22) respectively. The number 1 and the number itself would always be a factor of the given number.

Refer to the following table to check division 22 by its factors:

Factors of 22 By Prime Factorization

Prime Factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors.

Method 1: Division Method

To find prime factors of 22 using the division method,

• Step 1. Start dividing 22 from the smallest prime number i.e., 2, 3, 5, and so on. and find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 22 i.e., 2, divide 22 by 2 to obtain the quotient (11)

22 ÷ 2 = 11

• Step 3. Repeat step 1 with the obtained quotient (11). Again, the prime factor for 11 will be 11 ( since 11 is a prime number).

11 ÷ 11 = 1

So, the prime factorization of 121 is 22 = 2 × 11

Method 2: Factor Tree Method

We can do the same procedure using the factor tree for 22 as shown in the diagram given below:

So, the Prime factorization of 22 is 22 = 2 × 11

Further, find the products of the multiplicands in different orders to obtain the composite factors of the number.
Thus, the total factors can be written including both the prime and composite numbers together.

Hence, the factors of 22 are 1, 2, 11, and 22.

Explore factors using illustrations and interactive examples

• Factors of 23 - The factors of 23 are 1 and 23.
• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
• Factors of 225 - The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
• Factors of 224 - The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224.
• Factors of 33 - The factors of 33 are 1, 3, 11, and 33.

Factors of 22 in Pairs

Pair Factors are the factors of a number given in pairs, when multiplied together give that original number. The pair factors of 22 would be the two numbers when multiplied together, result in the value 22.
The following table represents the calculation of pair factors of 22:

Negative Pair Factors

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 22.
The negative factor pairs of 22 would be (-1, -22 ) and (-2, -11).

• The number 22 has 4 factors, which makes it a composite number.
• The largest prime factor for 22 is 11.
• The negative factor pairs of 22 are (-1, -22) and ( -2, -11).

Challenging Questions

• Two wires of length 22 inches and 16 inches are bought by an electrician. He wants to cut them into pieces of equal lengths. What is the maximum length of each piece possible for him to cut the wire into?