Factors of 1296

The factors of 1296 are the numbers that divide 1296 evenly.

Those factors are:

Positive Factors of 1296: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 54, 72, 96, 108, 144, 162, 216, 288, 432, 648, and 1296.

Negative Factors of 1296: Negative factors are simply the negative counterparts of the positive factors. These are:

Negative Factors:
-1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -54, -72, -96, -108, -144, -162, -216, -288, -432, -648, and -1296.

Prime Factors of 1296: Prime factors are the prime numbers that, when multiplied together, result in 1296.

Prime Factors of 1296: 2, 3.

Prime Factorization of 1296: Prime factorization is the process of breaking down 1296 into its prime factors.
 

It is expressed as 2⁴ × 3⁴ 

Table listing the factors of 1296:

This breakdown helps in understanding the various factors of 1296, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 1296. Below are some of the common methods:

Methods to Find the Factors of 1296:

1. Multiplication Method
2. Division Method
3. Prime Factorization
4. Factor Tree

The multiplication method involves finding pairs of numbers whose product is 1296.

Step 1: Find the pair of numbers whose product is 1296.

Step 2: The factors are those numbers that, when multiplied, give 1296.

Step 3: Make a list of numbers whose product will be 1296.

Here are some pairs of numbers whose product is 1296:
1 × 1296 = 1296
2 × 648 = 1296
3 × 432 = 1296
4 × 324 = 1296
6 × 216 = 1296
8 × 162 = 1296
9 × 144 = 1296
12 × 108 = 1296
16 × 81 = 1296
18 × 72 = 1296
24 × 54 = 1296

Thus, the factors of 1296 are:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296.

The division method finds the numbers that fully divide 1296.

Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 1296 ÷ 1 = 1296.

Step 2: Move to the next integers, checking for divisibility. Both the divisor and quotient are factors.

Picture showing the division method:

For example:
1296 ÷ 2 = 648 (So, 2 and 648 are factors)
1296 ÷ 3 = 432 (So, 3 and 432 are factors)
Continue until you have checked all integers up to √1296 ≈ 36.

Thus, the factors of 1296 are:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296.

Multiplying prime numbers to get the given number as their product is called prime factors. Prime factorization is breaking down the number into its prime factors. 

The prime factors of 1296 are 2 and 3.

Steps for Prime Factorization:

Divide 1296 by the smallest prime number, 2:
1296 ÷ 2 = 648
648 ÷ 2 = 324
324 ÷ 2 = 162
162 ÷ 2 = 81 (81 is not divisible by 2, so move to the next prime number, 3)
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

Prime Factorization of 1296:
1296 = 2⁴ × 3⁴

A factor tree visually represents the prime factorization. It helps to understand the factorization process easily.
Here’s how you break down 1296 into its prime factors using a factor tree:
 

Factors of 1296 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs of 1296:

(1, 1296), (2, 648), (3, 432), (4, 324), (6, 216), (8, 162), (9, 144), (12, 108), (16, 81), (18, 72), (24, 54), (36, 36)

Negative Factor Pairs of 1296:

(-1, -1296), (-2, -648), (-3, -432), (-4, -324), (-6, -216), (-8, -162), (-9, -144), (-12, -108), (-16, -81), (-18, -72), (-24, -54), (-36, -36)

These are the positive and negative factor pairs of 1296.

Co-prime: Numbers having 1 as the only common factor.
 

Perfect Square: The number we get when the same number is multiplied twice.
 

Prime Factors: Prime numbers, which are factors of a given number
 

Factor Tree: A tree diagram used to represent the prime factors of a given number.
 

Multiple: Numbers we get when another number multiplies the given number.