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# Factors of 72

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Do you know the factors? A factor is a number/algebraic expression that completely divides another number evenly with no remainder.

Understanding the factors of numbers is pivotal in mathematics, shaping everything from elementary arithmetic to intricate algebra. In this enlightening piece, we’ll focus on the factors of the number 72 using two elementary methods: Prime Factorization and the Factor Tree Method.

### What Are the Factors of 72?

The factors of 72 are the whole numbers that, when multiplied, produce the value of 72.

In other words, they are the numbers that divide 72 seamlessly, leaving no remainder. The numbers that are factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, & 72. Recognizing factors is imperative in mathematics, as they unravel numbers into their essential components, rendering them simpler to handle.

### How to Find the Factors of 72?

Factors of 72 are straightforward with these two chief techniques

#### 1. Using Prime Factorization

Prime factorization decomposes a number into prime numbers, which are indivisible except by 1 or themselves. This technique uncovers the fundamental elements of a number. Every number can be represented as a product of these prime numbers uniquely (although the sequence of numbers might differ). This technique is instrumental in mathematics, aiding in various domains like equation solving and comprehension of numerical behavior.

Step 1: Begin with the Smallest Prime Number

Divide 72 by 2: 72÷2=36

Divide 36 by 2: 36÷2=18

Divide 18 by 2: 18÷2=9

Divide 9 by 3: 9÷3=3

Step 2: Draft the Prime Factorization The prime factorization of 72 is:

72=2×2×2×3×3

Step 3: Enumerate the Factors

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

#### 2. Using a Factor Tree

A Factor Tree is an illustrative tool that demonstrates how a number decomposes into prime numbers. Commencing with your main number, keep halving it, designing branches as you would see on a tree. Continue until you arrive at numbers that can’t be further divided, except by 1 or themselves – these are the prime numbers. The Factor Tree simplifies the visualization of how prime numbers amalgamate to compose a larger number.

Step 1: Start with 72, and pick 2 as a factor since 72 is even:

72

/ \

2   36

Step 2: Noticing 36 is even, divide it by 2:

72

/  \

2    36

/ \

2   18

Step 3: 18 is still even, divide by 2:

72

/  \

2    36

/  \

2    18

/  \

2    9

Step 4: Now, 9 is divisible by 3:

72

/  \

2    36

/  \

2    18

/  \

2     9

/ \

3   3

From the factor tree, we can deduce that the prime factorization of 72 is: 2×2×2×3×3.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

### Summary

Through this illuminating exposition, we’ve unearthed how to adeptly pinpoint the factors of 72 utilizing prime factorization and factor trees.

Whether you’re a student, educator, or simply a math enthusiast, mastering these methodologies can elevate your mathematical prowess and insights.

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