Factors of 84
by Lily, Aug 07 2023
Unveiling the Magic of Factors
In the realm of mathematics, factors play a significant role in understanding how numbers come into being. Factors are the mystical numbers that can be multiplied together to create a given number. Each number has its own unique set of factors, and some are more special than others.
Let's see some examples to grasp this magical concept!
- For the number 1, the only factor is 1.
- For the number 6, the factors are 1, 2, 3, and 6.
Embracing the Marvel of Prime Numbers
Within the vast universe of numbers, some hold an extraordinary secret. These rare beings have only two factors: 1 and the number itself. These mystical numbers are known as prime numbers!
Let's meet some of these enchanting entities!
- 1 has only 1 as its factor.
- 2 has 1 and 2 as its factors.
- 3 has 1 and 3 as its factors.
- 5 has 1 and 5 as its factors.
- 7 has 1 and 7 as its factors.
Seeking the Factors of 84
Now, let us embark on the quest to discover the factors of the captivating number 84! To find its factors, we shall endeavor to multiply different numbers and witness the magical product of 84!
Let the journey begin!
- 1 x 84 = 84
- 2 x 42 = 84
- 3 x 28 = 84
- 4 x 21 = 84
- 6 x 14 = 84
- 7 x 12 = 84
Behold! We have discovered the mystical factor pairs of 84: (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), and (7, 12)! What an enchanting revelation!
Our thrilling quest has led us to meet the unique numbers that beautifully constitute the magical 84. Let us welcome them with open arms!
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84!
Unraveling the Secret of Prime Factorization
Now, let us unlock the hidden code of prime factorization for our beloved number 84! We shall divide it by prime numbers to reveal its prime factors. Brace yourselves for this mystical journey!
- Step 1: Begin with the number 84.
- Step 2: Divide by the smallest prime factor: 2 84 ÷ 2 = 42
- Step 3: Divide the quotient 42 by the smallest prime factor again.
42 ÷ 2 = 21
- Step 4: Divide the new quotient 21 by the smallest prime factor.
21 ÷ 2 = 10.5
Since 10.5 is not a whole number, we must move on to the next smallest prime number: 3
21 ÷ 3 = 7
- Step 5: Divide the new quotient 7 by the smallest prime factor (or continue until you reach a whole number).
- 7 ÷ 2 = 3.5
- 7 ÷ 3 = 2.33
- 7 ÷ 5 = 1.4
- 7 ÷ 7 = 1
At last, we have reached the final quotient of 1. Thus, the prime factorization of 84 is 2 x 2 x 3 x 7, or in exponent form, 2² x 3 x 7! Such a wondrous revelation!
Unfolding the Enchanting Factor Tree of 84
Behold the mesmerizing factor tree of 84! It reveals the mystical journey of factorization, with the prime factors standing tall at the bottom and the majestic 84 reigning above all!
According to the factor tree:
84 = 4 × 21 = (2 × 2) × (3 × 7)
The Power of Factors in Our Daily Lives
Mastering the art of factoring can be truly magical in our everyday adventures. It empowers us to divide and conquer, make quick calculations, and explore the hidden gems of numbers. Whether shopping, traveling, or managing finances, the wisdom of factors guides us like a celestial compass!
Conclusion
Congratulations, brave explorers! You have unlocked the mysteries of factors and delved into the wonders of 84! As you continue your odyssey through the realm of mathematics, embrace the spirit of curiosity, and let the magic of numbers inspire your quest for knowledge! The cosmos of math awaits your exploration! Happy exploring ahead!