Factors of 1539

The numbers that divide 1539 evenly are known as factors of 1539. A factor of 1539 is a number that divides the number without remainder. The factors of 1539 are 1, 3, 9, 13, 39, 51, 117, 171, 513, and 1539.

Negative factors of 1539: -1, -3, -9, -13, -39, -51, -117, -171, -513, and -1539.

Prime factors of 1539: 3 and 13.

Prime factorization of 1539: 3² × 13 × 13.

The sum of factors of 1539: 1 + 3 + 9 + 13 + 39 + 51 + 117 + 171 + 513 + 1539 = 2456

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

1. Finding factors using multiplication
2. Finding factors using the division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1539. Identifying the numbers which are multiplied to get the number 1539 is the multiplication method.

Step 1: Multiply 1539 by 1, 1539 × 1 = 1539.

Step 2: Check for other numbers that give 1539 after multiplying   

3 × 513 = 1539

9 × 171 = 1539

13 × 117 = 1539    

39 × 39 = 1539

Therefore, the positive factor pairs of 1539 are: (1, 1539), (3, 513), (9, 171), (13, 117), (39, 39). All these factor pairs result in 1539. For every positive factor, there is a negative factor.

Dividing the given numbers with the 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 1539 by 1, 1539 ÷ 1 = 1539.

Step 2: Continue dividing 1539 by the numbers until the remainder becomes 0.

1539 ÷ 1 = 1539

1539 ÷ 3 = 513

1539 ÷ 9 = 171

1539 ÷ 13 = 117

1539 ÷ 39 = 39

Therefore, the factors of 1539 are: 1, 3, 9, 13, 39, 51, 117, 171, 513, 1539.

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 1539 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1539 ÷ 3 = 513

513 ÷ 3 = 171

171 ÷ 3 = 57

57 ÷ 3 = 19

19 ÷ 19 = 1

The prime factors of 1539 are 3 and 19. The prime factorization of 1539 is: 3² × 19.

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

Step 1: Firstly, 1539 is divided by 3 to get 513.

Step 2: Now divide 513 by 3 to get 171.

Step 3: Then divide 171 by 3 to get 57.

Step 4: Divide 57 by 3 to get 19. Here, 19 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1539 is: 3² × 19.

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 1539: (1, 1539), (3, 513), (9, 171), (13, 117), and (39, 39).

• Negative factor pairs of 1539: (-1, -1539), (-3, -513), (-9, -171), (-13, -117), and (-39, -39).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1539 are 1, 3, 9, 13, 39, 51, 117, 171, 513, and 1539.

• Prime factors: The factors which are prime numbers. For example, 3 and 19 are prime factors of 1539.

• 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 1539 are (1, 1539), (3, 513), etc.

• Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 1539 is 3² × 19.

• Multiple: A multiple of a number is the product of that number and an integer. For example, 1539 is a multiple of 9.