Factors of 189

The factors of 189 are the numbers that divide 189 exactly without leaving any remainder. The numbers 1, 3, 7, 9, 21, 27, 63, and 189 are the factors of 189.

Negative Factors of 189: Negative factors are the opposite of positive factors. For 189, they are  -1, -3, -7, -9, -21, -27, -63, and -189.

Prime Factors of 189: The prime numbers of 189 are 3 and 7, as it is the only prime number that divides it evenly without any remainder.

Prime Factorization of 189: Prime factorization is the breakdown of a number into its prime factors. For 189, the prime factor is 3³ × 7
 

We can find the factors by dividing the number completely or by using its factors. The following are the ways by which we can find the factors

In this method, we will try to find such pairs of numbers, in which the product of the pair would give the original number as the result. We should follow the steps mentioned below to find the factors.

Step 1 : Identify a pair of numbers whose product equals 189.

Step 2 : List such pairs of numbers one by one. 

Here, the factor pairs of 189 are (1, 189), (3, 63), (7, 27), and (9, 21).
 

In the division method, we need to find such numbers that will divide a number evenly without leaving any remainder.

189 ÷ 1 = 189
189 ÷ 3 = 63
189 ÷ 7 = 27
189 ÷ 9 = 21
189 ÷ 21 = 9
189 ÷ 27 = 7
189 ÷ 63 = 3
189 ÷ 189 = 1

To find the factors of 189 using the division method, 189 is first divided by 1 and continues upon. The numbers 1, 3, 7, 9, 21, 27, 63, and 189 are the factors of 189.
 

In the method of prime factorization, a number is expressed as a product of its prime factors. For example, 189 is expressed as 3³ × 7. Here, 3 and 7 are the prime numbers that would divide 189 evenly. Hence, they are called the prime factors of 189.

Factor Tree:

A factor tree is a diagrammatic representation that breaks down the prime factors of the given number.

Factor Pairs:

The factor pairs of a number refer to the pairs of numbers which, when multiplied, will give the original number as a product.

Positive pair factors of 189 are (1, 189), (3, 63), (7, 27), and (9, 21).

Negative pair factors of 189 are (-1, -189), (-3, -63), (-7, -27), and (-9, -21).
 

• Prime Numbers: The numbers that have only 2 factors 1 & the number itself are called Prime Numbers. For example: If we take the number 3, we will get the prime factorization of 1 × 3, therefore it is a prime number.

• Composite Numbers: composite numbers are the numbers that have more than 2 factors. For example: The composite number of 10 is 1, 2, 5, and 10

• Negative Factors: These numbers are the negative counterparts of the positive factors of a number. For example: the negative factor of 10 is, -1, -2, -5, -10.

• Factor Tree: A factor tree is a graphical representation of breaking down a composite number into prime factors.

• Multiple: In mathematics, a multiple means the number which can be divisible by another number without leaving any remainder. For example: 4 × 1 = 4