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Factors Of 90

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Unlocking the Secrets of 90: A Comprehensive Guide to its Factors



Understanding factors is a fundamental concept in mathematics, essential for grasping more advanced topics like prime factorization, fractions, and algebra. This article will delve into the factors of 90, a seemingly simple number that offers a rich opportunity to explore this important mathematical idea. We'll break down the process step-by-step, using clear explanations and practical examples to make the learning experience engaging and accessible.


What are Factors?



A factor is a number that divides another number exactly, without leaving a remainder. In simpler terms, if you can divide a number by another number and get a whole number result, then the number you divided by is a factor. For example, the factors of 6 are 1, 2, 3, and 6, because 6 can be divided evenly by each of these numbers. We can represent this as 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1.


Finding the Factors of 90: A Systematic Approach



To find all the factors of 90, we can use a methodical approach. We start by checking each number, beginning from 1, to see if it divides 90 without leaving a remainder.

1. Start with 1: Every number has 1 as a factor. 90 ÷ 1 = 90. So, 1 and 90 are factors.
2. Check for 2: 90 is an even number, so it's divisible by 2. 90 ÷ 2 = 45. Thus, 2 and 45 are factors.
3. Check for 3: The sum of the digits of 90 (9 + 0 = 9) is divisible by 3, indicating that 90 is divisible by 3. 90 ÷ 3 = 30. So, 3 and 30 are factors.
4. Check for 4: 90 is not divisible by 4 because it doesn't end in a multiple of 4 (00, 04, 08, etc.).
5. Check for 5: 90 ends in 0, so it's divisible by 5. 90 ÷ 5 = 18. Hence, 5 and 18 are factors.
6. Check for 6: Since 90 is divisible by both 2 and 3, it's also divisible by 6. 90 ÷ 6 = 15. Therefore, 6 and 15 are factors.
7. Check for 7: 90 ÷ 7 = 12 with a remainder, so 7 is not a factor.
8. Check for 8: 90 is not divisible by 8.
9. Check for 9: 90 is divisible by 9 because 90 ÷ 9 = 10. Thus, 9 and 10 are factors.
10. Check for 10: We already found that 10 is a factor.


We've now systematically checked numbers up to 10. Notice that as we progress, we start finding factor pairs. Once we reach a factor (e.g., 10) whose pair (9) we’ve already found, we can stop. We’ve found all the factors.


The Complete List of Factors of 90



Therefore, the factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.


Practical Applications of Factors



Understanding factors is crucial in many real-life situations:

Dividing objects equally: Imagine you have 90 candies to distribute equally among friends. You can find out how many friends you can give candies to by considering the factors of 90.
Simplifying fractions: Factors are essential for simplifying fractions to their lowest terms. For example, the fraction 45/90 can be simplified using the common factor 45, reducing it to 1/2.
Solving algebraic equations: Finding factors is crucial in solving many types of algebraic equations.


Key Takeaways



Factors are whole numbers that divide a number without leaving a remainder.
A systematic approach helps identify all factors efficiently.
Understanding factors is fundamental to various mathematical concepts and real-world applications.



Frequently Asked Questions (FAQs)



1. What is the prime factorization of 90? The prime factorization of 90 is 2 x 3² x 5. This means 90 is composed of only prime numbers multiplied together.

2. How many factors does 90 have? 90 has 12 factors.

3. Are all factors of 90 even numbers? No, several factors of 90 are odd numbers (1, 3, 5, 9, 15, 45).

4. Is there a quicker method to find factors than the one described? While the systematic approach is reliable, more advanced techniques like factor trees and prime factorization can be used for larger numbers to find factors more quickly.

5. Why is understanding factors important in higher-level mathematics? Factors are essential for understanding concepts like greatest common divisor (GCD), least common multiple (LCM), and polynomial factorization, all crucial in algebra and number theory.

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What is the prime factorization of 90? - Socratic 7 Apr 2016 · Using the smallest prime, 2, divide 90. #90/2=45# The smallest prime will not go into 45, so divide by the next smallest prime, 3.

How do you calculate dilution factor? + Example - Socratic 22 Mar 2014 · You divide the final volume by the initial volume. "DF" = V_f/V_i EXAMPLE 1: What is the dilution factor if you add a 0.1 mL aliquot of a specimen to 9.9 mL of diluent?

What are the factors of 90? - Socratic 7 Mar 2018 · When dealing with factors, you can list all the factors, or write a number as the product of the prime factors. If you know the product of the prime factors you can use those to determine all the other factors. #90 = 10 xx9# #:. 90 = 2xx5xx3xx3 " "= 2xx3xx3xx5# Listing the factors using these prime factors can be done as follows:

Factoring Completely - Algebra - Socratic What are the factors of #12x^3+12x^2+3x#? How do you find the two numbers by using the factoring method, if one number is seven more than the other and the product of two positive numbers is 120? How do you factor #12c^2-75# completely?

What is the GCF of 75 and 90? - Socratic 15 Oct 2016 · 15 The simplest way to find the Greatest Common Factor is as follows: Find one Common Factor Divide by that factor Look for a Common Factor in the new set of numbers Divide by that factor Repeat until you arrive at a dead end Gather all of the factors that you used and multiply them together. You should have the GCF now. Your Question: GCF of 75 and 90 …

What are all the greatest common factors of 36 and 90? 12 Sep 2016 · GCF = 18 Common factors: " " 1 , 2, 3, 6, 9, 18 There can be several common factors, but there is only one Greatest Common factor.

What types of external factors can influence an ecosystem? 31 Dec 2015 · There are multiple external factors that will affect an ecosystem. In reference to the field of Earth Science specifically and factors that are external to the ecosystem, earthquakes, volcanic eruptions, landslides, avalanches, loss of glacial mass, and others can all affect an ecosystem. Some of these effects will be drastic, such as a landslide that started at a higher …

How do you calculate serial dilutions? + Example - Socratic 18 Jun 2014 · You multiply the original concentration by the dilution factors for each dilution. A serial dilution is any dilution in which the concentration decreases by the same factor in each successive step. In serial dilutions, you multiply the dilution factors for each step. The dilution factor or the dilution is the initial volume divided by the final volume. DF = V_i/V_f For …

The number 90^9 has 1900 different positive integral ... - Socratic 21 Jul 2016 · Therefore, we have 5 possible ways to configure a divisor of 90^9 that is a square of an integer, using 5s alone. The same reasoning applies to 3^18 and 2^9. Every even power of these prime factors - 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 (10 total) for 3 and 0, 2, 4, 6, 8 (5 total) for 2 - is a perfect square who is a divisor of 90^9.

What is the GCF of 42 and 90? - Socratic 1 Dec 2017 · 6 Factors of 42: 1*42, 2* 21, 3*14, color(red)6*7. Factors of 90: 1* 90, 2* 45, 3* 30, 5* 18, color(red)6*15, 9*10.