Gcf of 30 and 105

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GCF of 30 and 105

FAQs on GCF of 30 and 105

What is the GCF of 30 and 105?

The GCF of 30 and 105 is 15. To calculate the GCF (Greatest Common Factor) of 30 and 105, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105) and choose the greatest factor that exactly divides both 30 and 105, i.e., 15.

If the GCF of 105 and 30 is 15, Find its LCM.

GCF(105, 30) × LCM(105, 30) = 105 × 30
Since the GCF of 105 and 30 = 15
⇒ 15 × LCM(105, 30) = 3150
Therefore, LCM = 210
☛ Greatest Common Factor Calculator

How to Find the GCF of 30 and 105 by Prime Factorization?

To find the GCF of 30 and 105, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 105 = 3 × 5 × 7.
⇒ Since 3, 5 are common terms in the prime factorization of 30 and 105. Hence, GCF(30, 105) = 3 × 5 = 15
☛ Prime Number

What are the Methods to Find GCF of 30 and 105?

There are three commonly used methods to find the GCF of 30 and 105.

  • By Long Division
  • By Listing Common Factors
  • By Prime Factorization

How to Find the GCF of 30 and 105 by Long Division Method?

To find the GCF of 30, 105 using long division method, 105 is divided by 30. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 30, 105?

The following equation can be used to express the relation between LCM and GCF of 30 and 105, i.e. GCF × LCM = 30 × 105.

 

Sours: https://www.cuemath.com/numbers/gcf-of-30-and-105/




On this page we will define the GCF of 30 and 105, teach you the different ways of calculating the GCF of 30 and 105, and show you what you can use the GCF of 30 and 105 for.

What is the GCF of 30 and 105?
GCF is the abbreviation for Greatest Common Factor. Therefore, the GCF of 30 and 105 is the same as the Greatest Common Factor of 30 and 105. The GCF of 30 and 105 is the largest positive integer by which both 30 and 105 can be divided. Furthermore, both 30 and 105 have a set of factors and the GCF is the greatest factor that 30 and 105 have in common.




Compare factors to get GCF of 30 and 105
Per definition above, to find the GCF of 30 and 105, you can compare the factors of 30with the factors of 105to see which factor is the greatest. When we did that, we found that the Greatest Common Factor (GCF) of 30 and 105 is 15.



Use LCM to get GCF of 30 and 105
The Least Common Multiple (LCM) of 30 and 105 is 210. You can find the GCF of 30 and 105 by dividing the product of 30 and 105 by the LCM of 30 and 105. Here is the formula and math:

  
Product of 30 and 105
 
  
LCM of 30 and 105
 
  =  GCF

  
30 × 105
 
  
210
 
  =  15



Use computer spreadsheet to get GCF of 30 and 105
If you have a computer, you can also use a spreadsheet in Excel or Numbers to calculate the GCF of 30 and 105. You want to type =gcf(30, 105) into a cell to get the answer.

gcf(30, 105) = 15




Use the GCF of 30 and 105 to simplify a fraction
The GCF of 30 and 105 can be used for many things. You can, for example, simplify a fraction by dividing the numerator and denominator by the GCF like this:

  
30 ÷ 15
 
  
105 ÷ 15
 
  = 
  
2
 
  
7
 
   



Use GCF of 30 and 105 to simplify a ratio
Similarly, you can use the GCF of 30 and 105 to simplify a ratio by dividing each part of the ratio by the GCF like this:

= 30 : 105
= (30 ÷ 15) : (105 ÷ 15)
= 2 : 7



Use the GCF of 30 and 105 to find the LCM of 30 and 105
Since using the Least Common Multiple (LCM) is one of the ways to find the GCF of 30 and 105, you can use the GCF of 30 and 105 to find the LCM of 30 and 105. The LCM of 30 and 105 can, for example, be used to add and subtract fractions with denominators of 30 and 105. The LCM of 30 and 105 is the product of 30 and 105 divided by the GCF of 30 and 105. Here is the math:

  
Product of 30 and 105
 
  
GCF of 30 and 105
 
  =  LCM

  
30 × 105
 
  
15
 
  =  210

That is all there is to it! We hope this page accomplished its goal of defining the GCF of 30 and 105 by showing you how to calculate the GCF, examples of its uses, and how it relates to LCM.

GCF Calculator
Use the GCF Calculator to solve a problem similar to the one explained on this page.

GCF of 30 and 106
Here is the next GCF on our list that we have calculated and explained for you.


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What is the greatest common factor of 30 and 105?

How to find the Greatest Common Factor

GCF example:

The first step is to find all divisors of each number. For instance, let us find the gcf(30, 105).

In this case we have:

  • The factors of 30 (all the whole numbers that can divide the number without a remainder) are 1, 2, 3, 5, 6, 10, 15 and 30;
  • The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.

The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 30 and 105 is 15. The GCF is the largest common positive integer that divides all the numbers (30, 105) without a remainder.

The GCF is also known as:

  • Greatest common divisor (gcd);
  • Highest common factor (hcf);
  • Greatest common measure (gcm), or
  • Highest common divisor

Greatest Common Factor Calculator

Greatest Common Factor Calculator

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gcf of 30 and 42 - Surendra Khilery - Lcm And Hcf - Prime Factorisation Method - Surendra Khilery

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Of 105 and gcf 30

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Common Factoring; Factoring Polynomials using Greatest Common Factor(GCF).Algebra

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