Do you know that 189 can be expressed as the sum of cubes of 4 and 5? It can also be expressed as sum of cubes of 6 and (-3). In this chapter, we will calculate the factors of 189, prime factors of 189, and factors of 189 in pairs along with solved examples for a better understanding.
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|1.||What Are the Factors of 189?|
|2.||How to Calculate Factors of 189?|
|3.||Factors of 189 by Prime Factorization|
|4.||Factors of 189 in Pairs|
|5.||FAQs on Factors of 189|
What Are the Factors of 189?
The factors of 189 are the numbers which on multiplication give the product as 189. In other words, factors of 189 are numbers which leave no remainder when 189 is divided by them. So, when any two whole numbers are multiplied with each other and 189 is obtained as the answer, it is said that both these numbers are the factors of 189.
How to Calculate the Factors of 189?
To calculate the factors of 189, we find all the numbers which would divide 189 without leaving any remainder. 189 can be expressed as a product of its prime factors in the prime factorization method and hence we divide 189 with its divisors in the division method. For the numbers which divide 189 entirely, the divisors, as well as their quotients, are the factors of 189.
|189/1 = 189||1 and 189 are factors of 189.|
|189/3 = 63||3 and 63 are factors of 189.|
|189/7 = 27||7 and 27 are factors of 189.|
|189/9 = 21||9 and 21 are factors of 189.|
Hence, the factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189.
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Factors of 189 by Prime Factorization
When a composite number is expressed as the product of its prime factors, it is known as prime factorization.To get the prime factorization of 189, we use two methods:Method 1: Factor Tree MethodMethod 2: Upside-Down Division Method
Method 1: Factor Tree Method
The factor tree for 189 is:
Method 2: Upside-Down Division Method
On dividing 189 by its smallest prime factor which is 3, we get
189/3 = 63
63 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1. The prime factorization of 189 is shown as:
Hence, the prime factors of 189 are 3 and 7. The prime factorization of 189 is 3 × 3 × 3 × 7.
Factors of 189 in Pairs
The pairs of numbers which on multiplication give 189 are the factor pairs of 189. Observe the following factors of 189 in pairs. If we consider negative integers, then the numbers in the pair factors will be negative as ( - ve × - ve ) = +ve.
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Important Notes:As the sum of digits of 189 is 18, 3 and 9 are the factors of 189.189 is a non-perfect square number. Hence, it has even number of factors.