Study Guide · Maths

What are the Factors of 96?

As numbers get larger, they often have many more factors. 96 is a highly divisible number, which means it has a long list of numbers that can divide it perfectly without a remainder.

Question (Click to Flip)

What are the first 5 multiples of 96?

Answer

Do not confuse factors (which are smaller) with multiples (which are larger). The multiples are the 'times table' of 96: 96, 192, 288, 384, and 480.

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Key Facts

We know 96 is divisible by 6 because it passes two rules: It is an even number (divisible by 2), and its digits add up to 15 (which is divisible by 3). If a number is divisible by both 2 and 3, it is automatically divisible by 6.

96 is often used in mathematical logic puzzles because of its large number of factors.

1. What are the Factors of 96?

Because it is a highly composite even number, 96 has exactly 12 positive factors. The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

2. Finding the Factor Pairs

To make sure we didn't miss any numbers, let's pair them up. These pairs multiply to exactly 96:

$1 \times 96 = 96$
$2 \times 48 = 96$
$3 \times 32 = 96$
$4 \times 24 = 96$
$6 \times 16 = 96$
$8 \times 12 = 96$

3. Prime Factorization of 96

Let's build a 'Factor Tree' to break 96 down into pure prime numbers. We will keep dividing by 2 until we hit an odd number:

$96 \div 2 = 48$
$48 \div 2 = 24$
$24 \div 2 = 12$
$12 \div 2 = 6$
$6 \div 2 = 3$
3 is a prime number, so the tree stops. The prime factorization of 96 is: $2 \times 2 \times 2 \times 2 \times 2 \times 3$ (or $2^5 \times 3$).

Questions and Answers

What are the first 5 multiples of 96?+

Do not confuse factors (which are smaller) with multiples (which are larger). The multiples are the 'times table' of 96: 96, 192, 288, 384, and 480.

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