Learn How to Factorize 32 and 21 in Detail

Sansar LochanCSAT, Guest PostLeave a Comment

Factors in mathematics are positive integers that can divide a number evenly. Assume we want to get a product by multiplying two numbers. The factors of the product are the multiplied numbers. Each number is a multiplier of itself. There are several real-life examples of factors, such as placing candy in a box, arranging numbers in a pattern, distributing chocolates to kids, and so on. To find the factors of a number, we need to use the multiplication or prime factorization method.

These are the numbers that can precisely divide a number. As a result, there is no remainder after division. Factors are integers that when multiplied together yield another number. A factor is thus the divisor of another number.

Factorisation is defined in mathematics as the process of dividing a number into a product of factors that, when multiplied together, yield the original number. For example, the factorization of 32 gives us factor pairs (1, 32), (2, 16), (4,8). From this, we can easily get the factors of 32, which are 1, 2, 4, 8, 16 and 32.

Let’s learn about factorization in more detail by taking two numbers i.e., 21 and 32 as examples.

Factorization of 21

The factors of 21 are the integers that, when multiplied together, yield the result 21. A number factor divides the original number uniformly.

Pair Factors of 21

To find the pair factors of 21, add the two numbers together to get the original number. As shown below, we can write both positive and negative integers in pairs:

Positive pairs

1 × 21 = 21; (1, 21) 

3 × 7 = 21; (3, 7)      

7 × 3 = 21; (7, 3)      

21 × 1 = 21; (21, 1) 

As a result, the pair factors of 21 are (1, 21), (3, 7), (7, 3) and (21, 1).

The 21 factors are 1, 3, 7, and 21.

Prime Factors of 21

The term “prime factorization” refers to the process of expressing a composite number as the product of its prime components. We will use the following process to obtain the prime factorization of 21:

  • Divide 21 from its prime factor, say 3.

21 ÷ 3 = 7

  • The quotient is obtained by dividing 7 by its prime factor.
  • This method is repeated until the quotient equals one.

7 ÷ 7 = 1 

  • We discover that 21 has two prime factors i.e., 3 and 7.

Prime factors of 21 are 3 and 7.

Factors of 32

Factors of 32 are integers that can completely divide 32. If x is a factor of 32, then 32 must be evenly divisible by x. Because 32 is a composite number, it will have more than two factors.

Pair Factors of 32

To determine the factor pairs of 32, multiply the two integers in a pair to get the original number as 32, as shown below:

Positive Pair Factors

1 × 32 = 32 ⇒ (1, 32)

2 × 16 = 32 ⇒ (2, 16)

4 × 8 = 32 ⇒ (4, 8)      

The factors of 32 are 1, 2, 4, 8, 16 and 32.

What are the Prime Factors of 32?

The process of representing a composite number as the product of its prime factors is known as prime factorization.

  • To find the prime factorization of 32, divide it by its smallest prime factor, 32÷2 = 16.
  • The quotient is produced by dividing 16 by its smallest prime factor, 16÷2 = 8.
  • This process is repeated until the quotient equals 1.

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

32 in terms of the product of its prime factors can be expressed as 2 × 2 × 2 × 2 × 2.

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