Understanding the factors of a number is essential for various mathematical calculations and operations. The factors of a number are those numbers that can divide evenly, leaving no remainder. This article will delve into factor 48, the methods to find these factors and their significance in mathematics.
What Are the Factors of 48?
The factors of 48 are integers that divide 48 evenly without any remainder. Here are some numbers: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. As with any number, 1 and the number (48) are always factors. A number with more than two factors, such as 48, is a composite number.
Recommended Reading: Factors of 45
How to Find the Factors of 48?
There are two primary methods to determine the factors of a number:
1. Using Prime Factorization:
Prime factorization is a method to break down a number into its fundamental prime factors. These prime factors consist of prime numbers with the unique property of evenly dividing the original number.
To find the prime factorization of 48, follow these steps:
Step 1: Divide 48 by the smallest prime number, 2: 48 ÷ 2 = 24. Hence, 2 is a factor.
Step 2: Continue dividing 24 by 2: 24 ÷ 2 = 12. Hence, we get another 2 as a factor.
Step 3: Repeat this process and divide 12 by 2: 12 ÷ 2 = 6. Thus, another 2 is identified as a factor.
Step 4: Now, 6 is not divisible by 2 but by the following prime number, which is 3. Divide 6 by 3: 6 ÷ 3 = 2. Hence, we get 3 as another factor.
Step 5: Divide 2 by 2: 2 ÷ 2 = 1. Again, we obtain 2 as a factor.
Step 6: The prime factors obtained from this division process are 2, 2, 2, 2, and 3. We multiply these prime factors: 2 × 2 × 2 × 2 × 3 equals 48. This is the prime factorization of 48.
Hence, the prime factorization of 48 is 2 × 2 × 2 × 2 × 3, or in exponent form, 2⁴ × 3.
2. Using a Factor Tree:
A factor tree is a graphical representation used to determine the factors of a number. It breaks down the number into its prime factors, making it easier to recognize them.
Here are the steps to create a factor tree for 48:
Step 1: Start with the number 48 and draw a pair of branches beneath it.
4 8
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Step 2: Find a pair of factors of 48. The pair of factors for 48 are 2 and 24.
48
/ \
2 24
Step 3: Continue finding factors. The factors of 24 are 2 and 12.
48
/ \
2 24
/ \
2 12
Step 4: Continue finding factors. The factors of 12 are 2 and 6.
48
/ \
2 24
/ \
2 12
/ \
2 6
Step 5: Now, 6 is not divisible by 2, but it is divisible by 3. Divide 6 by 3: 6 ÷ 3 = 2.
48
/ \
2 24
/ \
2 12
/ \
2 6
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3
Step 6: Continue finding factors. The factors of 6 are 2 & 3.
48
/ \
2 24
/ \
2 12
/ \
2 6
/ \
2 3
Step 7: All the branches end with 2’s and 3’s.
Hence, the prime components of 48 are 2, 2, 2, 2, and 3.
Step 8: Now, we can find the factors of 48 by multiplying the combinations of the prime factors:
Factor’s of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
So, the factors 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, & 48.
Summary
In this blog article, we explored the factors of 48, which are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. We discussed two main methods to find these factors: prime factorization and factor trees. Prime factorization breaks 48 into prime factors (2 and 3), while a factor tree graphically displays them. Understanding these concepts and methods is valuable in various situations.
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