Factors of 1170

The numbers that divide 1170 evenly are known as factors of 1170. A factor of 1170 is a number that divides the number without remainder. The factors of 1170 are 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.

Negative factors of 1170: -1, -2, -3, -5, -6, -9, -10, -13, -15, -18, -26, -30, -39, -45, -65, -78, -90, -117, -130, -195, -234, -390, -585, and -1170.

Prime factors of 1170: 2, 3, 5, and 13.

Prime factorization of 1170: 2 × 3² × 5 × 13.

The sum of factors of 1170: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 13 + 15 + 18 + 26 + 30 + 39 + 45 + 65 + 78 + 90 + 117 + 130 + 195 + 234 + 390 + 585 + 1170 = 3384

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

1. Finding factors using multiplication
2. Finding factors using 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 1170. Identifying the numbers which are multiplied to get the number 1170 is the multiplication method.

Step 1: Multiply 1170 by 1, 1170 × 1 = 1170.

Step 2: Check for other numbers that give 1170 after multiplying

2 × 585 = 1170

3 × 390 = 1170

5 × 234 = 1170

6 × 195 = 1170

9 × 130 = 1170

10 × 117 = 1170

13 × 90 = 1170

15 × 78 = 1170

18 × 65 = 1170

26 × 45 = 1170

30 × 39 = 1170

Therefore, the positive factor pairs of 1170 are: (1, 1170), (2, 585), (3, 390), (5, 234), (6, 195), (9, 130), (10, 117), (13, 90), (15, 78), (18, 65), (26, 45), and (30, 39). 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 the simple division method -

Step 1: Divide 1170 by 1, 1170 ÷ 1 = 1170.

Step 2: Continue dividing 1170 by the numbers until the remainder becomes 0.

1170 ÷ 1 = 1170

1170 ÷ 2 = 585

1170 ÷ 3 = 390

1170 ÷ 5 = 234

1170 ÷ 6 = 195

1170 ÷ 9 = 130

1170 ÷ 10 = 117

1170 ÷ 13 = 90

1170 ÷ 15 = 78

1170 ÷ 18 = 65

1170 ÷ 26 = 45

1170 ÷ 30 = 39

Therefore, the factors of 1170 are: 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.

The factors can be found by dividing 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 1170 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1170 ÷ 2 = 585

585 ÷ 3 = 195

195 ÷ 3 = 65

65 ÷ 5 = 13

13 ÷ 13 = 1

The prime factors of 1170 are 2, 3, 5, and 13. The prime factorization of 1170 is: 2 × 3² × 5 × 13.

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

Step 1: Firstly, 1170 is divided by 2 to get 585.

Step 2: Now divide 585 by 3 to get 195.

Step 3: Then divide 195 by 3 to get 65.

Step 4: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1170 is: 2 × 3^2 × 5 × 13.

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 1170: (1, 1170), (2, 585), (3, 390), (5, 234), (6, 195), (9, 130), (10, 117), (13, 90), (15, 78), (18, 65), (26, 45), and (30, 39).
• Negative factor pairs of 1170: (-1, -1170), (-2, -585), (-3, -390), (-5, -234), (-6, -195), (-9, -130), (-10, -117), (-13, -90), (-15, -78), (-18, -65), (-26, -45), and (-30, -39).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1170 are 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 1170.

• 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 1170 are (1, 1170), (2, 585), etc.

• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1170 is 2 × 3² × 5 × 13.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For instance, 15 × 78 = 1170.