Factors of 93

The numbers that divide 93 evenly are known as factors of 93. A factor of 93 is a number that divides the number without a remainder. The factors of 93 are 1, 3, 31, and 93.

Negative factors of 93: -1, -3, -31, and -93.

Prime factors of 93: 3 and 31.

Prime factorization of 93: 3 × 31.

The sum of factors of 93: 1 + 3 + 31 + 93 = 128

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 93. Identifying the numbers which are multiplied to get the number 93 is the multiplication method.

Step 1: Multiply 93 by 1, 93 × 1 = 93.

Step 2: Check for other numbers that give 93 after multiplying     3 × 31 = 93

Therefore, the positive factor pairs of 93 are: (1, 93) and (3, 31).

All these factor pairs result in 93. 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 93 by 1, 93 ÷ 1 = 93.

Step 2: Continue dividing 93 by the numbers until the remainder becomes 0. 93 ÷ 1 = 93 93 ÷ 3 = 31

Therefore, the factors of 93 are: 1, 3, 31, 93.

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

93 ÷ 3 = 31

31 ÷ 31 = 1

The prime factors of 93 are 3 and 31. The prime factorization of 93 is: 3 × 31.

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

Step 1: Firstly, 93 is divided by 3 to get 31.

Step 2: Now divide 31 by 31 to get 1. Here, 31 is a prime number, and it cannot be divided anymore. So, the prime factorization of 93 is: 3 × 31.

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 93: (1, 93) and (3, 31).
• Negative factor pairs of 93: (-1, -93) and (-3, -31).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 93 are 1, 3, 31, and 93.

• Prime factors: The factors which are prime numbers. For example, 3 and 31 are prime factors of 93.

• 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 93 are (1, 93) and (3, 31).

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

• Division method: A method to find factors by dividing the original number by whole numbers to check for a remainder of zero.