Factors of 2079

The numbers that divide 2079 evenly are known as factors of 2079.

A factor of 2079 is a number that divides the number without a remainder.

The factors of 2079 are 1, 3, 9, 23, 69, 207, 693, and 2079.

Negative factors of 2079: -1, -3, -9, -23, -69, -207, -693, and -2079.

Prime factors of 2079: 3 and 23.

Prime factorization of 2079: 3² × 23 × 11.

The sum of factors of 2079: 1 + 3 + 9 + 23 + 69 + 207 + 693 + 2079 = 3084

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
   
• Finding factors using the division method
   
• Prime factors and prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 2079. Identifying the numbers which are multiplied to get the number 2079 is the multiplication method.

Step 1: Multiply 2079 by 1, 2079 × 1 = 2079.

Step 2: Check for other numbers that give 2079 after multiplying

3 × 693 = 2079

9 × 231 = 2079

23 × 90 = 2079

69 × 30 = 2079

Therefore, the positive factor pairs of 2079 are: (1, 2079), (3, 693), (9, 231), (23, 90), (69, 30).

All these factor pairs result in 2079.

For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 2079 by 1, 2079 ÷ 1 = 2079.

Step 2: Continue dividing 2079 by the numbers until the remainder becomes 0.

2079 ÷ 1 = 2079

2079 ÷ 3 = 693

2079 ÷ 9 = 231

2079 ÷ 23 = 90

2079 ÷ 69 = 30

Therefore, the factors of 2079 are: 1, 3, 9, 23, 69, 207, 693, 2079.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
   
• Using factor tree

Using Prime Factorization: In this process, prime factors of 2079 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

2079 ÷ 3 = 693

693 ÷ 3 = 231

231 ÷ 3 = 77

77 ÷ 7 = 11

11 ÷ 11 = 1

The prime factors of 2079 are 3, 7, and 11.

The prime factorization of 2079 is: 3² × 7 × 11.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 2079 is divided by 3 to get 693.

Step 2: Now divide 693 by 3 to get 231.

Step 3: Then divide 231 by 3 to get 77.

Step 4: Divide 77 by 7 to get 11.

Here, 11 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 2079 is: 3² × 7 × 11.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 2079: (1, 2079), (3, 693), (9, 231), (23, 90), and (69, 30).

Negative factor pairs of 2079: (-1, -2079), (-3, -693), (-9, -231), (-23, -90), and (-69, -30).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2079 are 1, 3, 9, 23, 69, 207, 693, and 2079.
   
• Prime factors: The factors which are prime numbers. For example, 3, 7, and 11 are prime factors of 2079.
   
• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 2079 are (1, 2079), (3, 693), etc.
   
• Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 2079 is 3² × 7 × 11.
   
• Division method: A method to find factors by dividing the number with integers and identifying divisors that give a remainder of zero. For example, using division to find factors of 2079.