Study About Factorization of Numbers Like 32 and 36 in Detail

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In mathematics, factors are positive integers that may divide a number evenly. Assume we wish to multiply two numbers to produce a product. The multiplied numbers are the product’s factors. Every number multiplies itself. Real-life instances of factors include putting candies in a box, arranging numbers in a pattern, giving chocolates to children, and so on. We must apply the multiplication or prime factorization method to find the factors of an integer.

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

In mathematics, factorisation is defined as the process of dividing a number into a product of factors that, when multiplied together, give the original number. For example, the factorization of 32 yields factor pairs (1, 32), (2, 16) and (4,8). This simply yields 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., 32 and 36 as examples.

Factors of 36

We know that a number’s factor completely divides the number. For example, the number 36 is composite and may be expressed as a unique product of primes, which is true prime factorization. A number like 36 has more than one factor; nonetheless, there is always one way to represent the number as a product of primes, which is why prime factorization is referred to as a unique product of primes. Let us now write out the various factors of 36.

36 = 36 x 1

      = 18 x 2

      = 12 x 3

      = 9 x 4 

      =  6 x 6

The factor pair of 36 are (1, 36),  (2, 18), (3, 12), (4, 9) and (6, 6)

How To Calculate Prime Factorization of 36?

To get the prime factorization of 36, start with the least prime number, which is 2. Divide it by two until it is entirely divisible by two. If a point is not divisible by two, use the next least prime integer, which is three. Continue using the same techniques until we get 1 as the quotient. Here is a step-by-step approach for calculating the prime factors of 36.

  • Divide 36 with 2

2 ÷ 36 = 18

  • Again divide the quotient (18) with 2

2 ÷ 18 = 9

  • Now the new quotient (9) is no more divisible by 2, try the next prime number i.e. 3

3 ÷ 9 = 3

  • Finally, divide 3 by itself to get 1.

3 ÷ 3 = 1

From the preceding procedures, we obtain a prime factor of 36 as 2 × 2 × 3 × 3 i.e. 22 × 32.

Factors of 32

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

Pair Factors of 32

To find the factor pairs of 32, multiply the two integers in a pair by 32 to get the original number:

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?

Prime factorization is the method of expressing a composite number as the product of its prime factors.

  • Divide 32 by its smallest prime factor, 32÷2 = 16., to obtain the prime factorization of 32.
  • By dividing 16 by its smallest prime factor, 16÷2 = 8, the quotient is obtained.
  • This is repeated until the quotient equals one.

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

32 can be represented as the product of its prime factors as 2 × 2 × 2 × 2 × 2.

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