Factors of 90
by Lily, Aug 07 2023
Hello, young math enthusiasts! Brace yourselves for an exhilarating escapade into the fascinating realm of factors. Think of factors as the secret codes that reveal the essence of numbers. Are you prepared to embark on this journey? Let's venture forth into the world of numbers with excitement and curiosity!
What Are Factors?
Picture this: factors are like special numbers that come together and make a fantastic multiplication magic! When we multiply certain numbers, we get another magical number! For example, with the number 6, we can use the factors 1 and 6, or 2 and 3, to unlock its mystery.
Let's try it!
- 1 x 6 = 6
- 2 x 3 = 6
Wow, it's like having secret codes to reveal the number 6!
Exploring the Factors of 90
Now, let's set our sights on the amazing number 90! Can you believe that 90 has a magical team of factors waiting to be discovered? Let's find them together!
- First, we'll try dividing 90 by different numbers, starting from 1 all the way up to 90. Here's what we get:
- 90 ÷ 1 = 90
- 90 ÷ 2 = 45
- 90 ÷ 3 = 30
- 90 ÷ 5 = 18
- 90 ÷ 6 = 15
- 90 ÷ 9 = 10
- 90 ÷ 10 = 9
- 90 ÷ 15 = 6
- 90 ÷ 18 = 5
- 90 ÷ 30 = 3
- 90 ÷ 45 = 2
- 90 ÷ 90 = 1
Ta-da! We've found the factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. That's an incredible team of factors! We know that factors also include negative integers. Therefore, we can also have a list of negative factors of 90, which are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.
Pair Factors of 90
Let's take it one step further and explore the pair factors of 90! Think of it as finding magical pairs of factors that, when multiplied, give us 90! Let's see what they are:
- 1 x 90 = 90
- 2 x 45 = 90
- 3 x 30 = 90
- 5 x 18 = 90
- 6 x 15 = 90
- 9 x 10 = 90
- 10 x 9 = 90
- 15 x 6 = 90
- 18 x 5 = 90
- 30 x 3 = 90
- 45 x 2 = 90
- 90 x 1 = 90
And don't forget the pairs with negative friends too:
- -1 x -90 = 90
- -2 x -45 = 90
- -3 x -30 = 90
- -5 x -18 = 90
- -6 x -15 = 90
- -9 x -10 = 90
Amazing! We've discovered the magical pairs of factors for 90!
Prime Factorization of 90
Now, let's reveal the secret code behind 90! The prime factorization of a number is like its unique DNA—it's a special combination of prime factors that can't be broken down any further.
Let's unveil it:
- Prime Factorization of 90:
- 90 = 2 x 3 x 3 x 5
- There it is! The magical DNA of 90 is 2 x 3 x 3 x 5!
The Magic Sum of Factors!
Hey, here's a cool math trick! Did you know that the sum of all factors of 90 is also magical?
Let's add them up and see what we get:
- 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234
- Wow! The magic sum of factors for 90 is 234!
Conclusion
In conclusion, factors are like special codes that help us understand and multiply numbers. They are numbers that, when multiplied together, give us a specific number. For example, the factors of 6 are 1 and 6, or 2 and 3. We can find factors by dividing the number. For 90, the factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Negative numbers can also be factors, like -2 or -10. Factors help us explore the knowledge of math and solve interesting puzzles!