Factors of 111

The numbers that divide 111 evenly are known as factors of 111. A factor of 111 is a number that divides the number without a remainder. The factors of 111 are 1, 3, 37, and 111

Negative factors of 111: -1, -3, -37, and -111.

Prime factors of 111: 3 and 37.

Prime factorization of 111: 3 × 37.

The sum of factors of 111: 1 + 3 + 37 + 111 = 152

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 111. Identifying the numbers which are multiplied to get the number 111 is the multiplication method.

Step 1: Multiply 111 by 1, 111 × 1 = 111.

Step 2: Check for other numbers that give 111 after multiplying 3 × 37 = 111

Therefore, the positive factor pairs of 111 are: (1, 111) and (3, 37). 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 111 by 1, 111 ÷ 1 = 111.

Step 2: Continue dividing 111 by the numbers until the remainder becomes 0.

111 ÷ 1 = 111

111 ÷ 3 = 37

Therefore, the factors of 111 are: 1, 3, 37, and 111.

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

111 ÷ 3 = 37

37 ÷ 37 = 1

The prime factors of 111 are 3 and 37. The prime factorization of 111 is: 3 × 37.

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

Step 1: Firstly, 111 is divided by 3 to get 37.

Step 2: Now divide 37 by 37 to get 1. Here, 37 is a prime number, that cannot be divided anymore. So, the prime factorization of 111 is: 3 × 37.

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 111: (1, 111) and (3, 37).
• Negative factor pairs of 111: (-1, -111) and (-3, -37).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 111 are 1, 3, 37, and 111.

• Prime factors: The factors which are prime numbers. For example, 3 and 37 are prime factors of 111.

• 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 111 are (1, 111) and (3, 37).

• Multiplication method: A method to find factors by identifying pairs of numbers multiplied to get the original number.

• Division method: A method to find factors by dividing the number by whole numbers to see which divisions result in whole numbers without a remainder.