What is HCF?

-
HCF and LCM > Important Formulas(HCF) Highest Common Factor(HCF) Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly. Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.

If you want to buy a book of HCF click here - CLICK

Highest Common Factor(HCF)
Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.
Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.
Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly.
We can find out HCF using prime factorization method or by dividing the numbers or division method.

Example 1: Find out HCF of 60 and 75
Step 1 : Express each number as a product of prime factors.
60 = 22 × 3 × 5
75 = 3 × 52

Example 2: Find out HCF of 36, 24 and 12
Step 1: Express each number as a product of prime factors.
36 = 22 × 32
24 = 23 × 3
12 = 22 × 3

How to find out HCF - by dividing the numbers (shortcut method)
Step 1: Write the given numbers in a horizontal line separated by commas.
Step 2: Divide the given numbers by the smallest prime number (write in the left side) which can exactly divide all the given numbers.
Step 3: Write the quotients in a line below the first.
Step 4: Repeat the process until we reach a stage where no common prime factor exists for all the numbers.
Step 5: We can see that the factors mentioned in the left side clearly divides all the numbers exactly and they are common prime factors. Their product is the HCF


Comments

Post a Comment

Popular posts from this blog

Molality, Molarity and Mole Fraction

-
Image
Molality, also called molal concentration, is a measure of the concentration of a solute in a solution in terms of amount of substance in a specified amount of mass of the solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. The properties and behavior of many solutions depend not only on the nature of the solute and solvent but also on the concentration of the solute in the solution. Chemists use many different units when expressing concentration; however, one of the most common units is molarity. Molarity (M) is the concentration of a solution expressed as the number of moles of solute per liter of solution. Mole fraction is another way of expressing the concentration of a solution or mixture. It is equal to the moles of one component divided by the total moles in the solution or mixture. a = the component that is being identified for mole fraction Mole fraction is used in a variety of calculations, b
Read more

What is Coulomb's Law?

-
Image
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The interaction between charged objects is a non-contact force that acts over some distance of separation. Charge, charge and distance. Every electrical interaction involves a force that highlights the importance of these three variables. Whether it is a plastic golf tube attracting paper bits, two like-charged balloons repelling or a charged Styrofoam plate interacting with electrons in a piece of aluminum, there is always two charges and a distance between them as the three critical variables that influence the strength of the interaction. In this section of Lesson 3, we will explore the importance of these three variables.                           Coulomb's Law equation The quantitative expre
Read more

What is Kirchhoff's law ?

-
Image
Kirchhoff's law Kirchhoff's laws  are two equalities that deal with the current and potential difference(commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called  Kirchhoff's rules  or simply  Kirchhoff's laws . These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the Circuits. Kirchhoffs First Law – The Current Law, (KCL) Kirchhoffs Current Law  or KCL, states that the “ total current or charge entering a junction or node
Read more