Factors of 96

Factors of 96 are numbers that, when multiplied in pairs give the product as 96. It has a total of 12 factors of which 96 is the biggest factor and the prime factors of 96 are 2 and 3. The sum of all factors of 96 is 252.

• Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96
• Negative Factors of 96: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48 and -96
• Prime Factors of 96: 2, 3
• Prime Factorization of 96: 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3
• Sum of Factors of 96: 252

We can use division to check whether 2, 4, 6, 16, 24, and 48 are factors of 96. As they leave no remainder, they are indeed the factors of 96.

Explore factors using illustrations and interactive examples:

• Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
• Factors of 97: The factors of 97 are 1 and 97.
• Factors of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
• Factors of 108: The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
• Factors of 6: The factors of 6 are 1, 2, 3, and 6.

There are two common methods to find the factors of 96:

1. Division method
2. Prime factorization method

Let us calculate the factors of 96 using the division method. Let's consider the numbers that can divide 96 without remainders. We will start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 48 (which is exactly half of 96).

Factorization means to write the number as a product of its factors. Prime Factorization refers to finding which prime numbers multiply together to form the original number.

• Step 1: Divide the number 96 with the smallest prime factor, say 2. 96 ÷ 2 = 48
• Step 2: Divide 48 again by 2. 48 ÷ 2 = 24
• Step 3: Divide 24 again by 2. 24 ÷ 2 = 12 and continue this division
• Step 4: 12 ÷ 2 = 6
• Step 5: 6 ÷ 2 = 3
• Step 6: Now if we will divide 3 by 2, we will get a fractional number and a factor cannot be a fraction or a decimal number. So, let's proceed with the next prime factor, say 3. 3 ÷ 3 = 1

The prime factors of 96 thus obtained are written as 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3¹, where 2 and 3 are the prime numbers.

Factor tree of 96

• The same division process is best represented in the form of a factor tree as given below:
• A factor tree is a special branching diagram where we find the factors of a number, then we find the factors of those numbers, etc. until we cannot factor anymore.
• The ends of a factor tree are all prime factors of the original number.

There are many ways of creating the factor tree of 96:

Pair factors of the number 96 are the whole numbers which when multiplied give the original number, i.e. 96. Pair factors could be either positive or negative. There are 12 pair factors of 96 and they are: (1,96), (-1,-96), (2,48), (-2,-48), (3,32), (-3,-32), (4,24), (-4,-24), (6,16), (-6,-16), (8,12), and (-8,-12).

Important Notes

• 96 is a composite number.
• 2 and 3 are the only prime numbers that are factors of 96.
• The number of factors of a given number is finite; 96 has a total of 12 factors.

• 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3¹
• To get the total numbers of factors of 96, simply add one to the exponent 5 and 1 and multiply their sums. (5 + 1) × (1 + 1) = 6 × 2 = 12
• Thus, 96 has 12 factors and they are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.