What are all the factors, the prime factorization, and factor pairs of 22?

Factors are the building blocks of numbers; they are the integers that we multiply together to arrive at a product. Taking 22 as an illustrative example, understanding the factors of this number helps us understand its properties and its role within mathematics. Factors are essential when simplifying fractions, finding least common multiples, and solving various mathematical problems.

The factors of a number include all whole numbers that can be multiplied in pairs to equal the number itself. For 22, this includes factors which, when paired, form the product of 22. A visual demonstration via multiplication is helpful to understand this:

• 1 x 22 = 22
• 2 x 11 = 22

The complete list of factors for 22 is relatively short:

• 1
• 2
• 11
• 22

Locating the factors of 22 can be achieved through division. The process involves dividing 22 by integers to see if the quotient is a whole number, in which case the divisor is a factor. We know every number is divisible by 1 and itself, so those are always factors. Since 22 is an even number, it is divisible by 2. By applying this division method, we can calculate its factors:

• 22 ÷ 1 = 22
• 22 ÷ 2 = 11
• 22 ÷ 11 = 2
• 22 ÷ 22 = 1

Dividing 22 by any other number results in a non-whole number, indicating that 1, 2, 11, and 22 are the only factors.

22’s pair factors are two numbers that, when multiplied, equal 22. Here’s a table showing both positive and negative pair factors:

The prime factorization of 22 is the process of breaking down 22 into its prime numbers. For 22, the prime factors are 2 and 11, since 2 is the smallest prime number that can divide 22, and 11 is a prime that results when 22 is divided by 2. Here’s the factor tree for visual understanding:

• 22 → 2 x 11

The prime numbers are circled in the following diagram:

• 22
• |
• 2, 11 (circled)

When discussing the factors of 22, here are some crucial points to bear in mind:

• There are 4 positive factors of 22: 1, 2, 11, 22.
• The only prime factors of 22 are 2 and 11.
• 22 has two pair factors: (1, 22) and (2, 11).
• The sum of all factors of 22 (1+2+11+22) is 36.

• What is the second smallest factor of 22?
• Write down the pair factors of 22.
• What two prime numbers multiply to 22?

Here are the solutions for the exercises:

• The second smallest factor of 22 is 2.
• The pair factors of 22 are (1, 22) and (2, 11).
• The two prime numbers that multiply to 22 are 2 and 11 (2 x 11).