We are writing a series of posts about factors to help you comprehend this mathematical topic and all of its complexities. In keeping with that, the focus of this blog will be on computing the factor of 60.
We will explore two primary methods to determine them:
- Prime Factorization
- Factor Tree Method
What Are the Factors of 60?
The factors of 60 are whole numbers that yield a product of 60 when multiplied together.
To elaborate, these numbers can be divided into 60 without leaving any remainder.
| Factors of 60 |
|---|
| 1, 2, 3, 4, 5, 6, 10,12, 15, 20, 30 and 60 |
Recognizing these factors is indispensable as it breaks down numbers into their core components, simplifying numerous mathematical tasks.
How to Determine the Factors of 60?
Pinpointing the factors of 60 is a breeze with the following chief techniques:
Using Prime Factorization
This method breaks down a number into its prime components—numbers that are divisible only by 1 and themselves.
Recommended Reading: Factors of 50
Through prime factorization, you can represent a number as a unique combination of prime numbers.
Step 1: Start with the Smallest Prime Number
Divide 60 by 2: 60 ÷ 2 = 30
Divide 30 by 2: 30 ÷ 2 = 15
Since 15 is not divisible by 2, divide 15 by 3: 15 ÷ 3 = 5
Step 2: Write Down the Prime Factorization
The prime factorization of 60 is given by: 60 = 2 × 2 × 3 × 5
Step 3: List Down the Factors
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 & 60.
Using a Factor Tree
A Factor Tree visually represents the decomposition of a number into its prime factors. Starting with the given number, keep dividing it until you reach prime numbers, constructing branches akin to a tree.
Step 1: Begin with 60 and select 2 as a factor, as 60 is even:
60
/ \
2 30
Step 2: 30 is also even, so we divide it by 2:
60
/ \
2 30
/ \
2 15
Step 3: Now, split 15 into its prime factors:
60
/ \
2 30
/ \
2 15
/ \
3 5
From this tree, the prime factorization of 60 becomes evident: 2 × 2 × 3 × 5.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 & 60.
Summary
This guide has equipped you with the knowledge to adeptly discern the factors of 60 using the twin techniques of prime factorization and factor trees. Whether you’re an educator, student, or just someone with a penchant for mathematics, these strategies will surely augment your mathematical understanding and dexterity.
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