Factors of 72

Hi Friends, Good Morning!!!

In our previous blog we learned about Factor of 28. Today let us learn about "Factor of 72"

Like concepts presented throughout the Montessori classroom, even those more abstract concepts of Mathematics have been made concrete for the children in our classrooms. Beginning with simple number concepts like understanding quantity and identifying numerals, the Math materials include advanced presentations in cubing numbers, factors, fractions, and mathematical operations.

Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.

Steps to draw the Factor Tree of 72

Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.

Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.

Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18

Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime

Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.

Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3

Step 7: On dividing it by 3 we get 3 which is the last and final factor.

Note: we keep on continuing these steps until we get all prime numbers in bottom row.

The Graphical representation of the factors of any number is called a Factor Tree

Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.

Steps to draw the Factor of 72

Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.

Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.

Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18

Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime

Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.

Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3

Step 7: On dividing it by 3 we get 3 which is the last and final factor.

Note: we keep on continuing these steps until we get all prime numbers in bottom row.

In the above figure on the left side we see all the prime factors

So the prime factorization can be written as product of all Prime factors

72= 2 x 2 x 2 x 3 x 3

In simplified form it can be written in form of Exponents

72= 2^3 x 3^2

I hope the above explanation was useful.Keep reading and leave your comments.

vertex formula

Hi Friends, Good Afternoon!!!

Let us learn about "vertex formula".

Introduction to write quadratic function in vertex form

General form of a quadratic equation is y= ax²+ bx +c where a,b and c are real numbers and a 0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)²+k.

There are 2 methods to write quadratic equation in vertex form.

Click on the link to learn about "quadratic equation formula"

1. Using completing the square method

2. Using vertex formula

VERTEX : For any two edges that meet at an end – point, there is a third edge, that also meets them at that end – point. This point of intersection of three edges of a cuboid is called a vertex of the cuboid.

The vertices of the cuboid in the figure are A, B, C, D, E, F, G, H.

Clearly, a cuboid has 8 vertices.

Thus, we see that the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length. This means that twelve edges of a cuboid can have only three distinct lengths. Usually, the longest of these is called the length of the cuboid and out of the remaining two, one is called the breadth or width and the other height of the cuboid.

BASE AND LATERAL FACES : Any face of a cuboid may be called the base of the cuboid. In that case, the four faces which meet the base are called the lateral faces of the cuboid.

I hope the above explanation was useful.Keep reading and leave your comments.

Antiderivative Calculator

Hi Friends, Good Afternoon!!!

Let us learn about "Antiderivative Calculator" and as you know in previous blog we learned about "Molarity Calculator" which was very interesting.

Antiderivative Calculator allows users to enter an integrand in order to return the indefinite integral. Does anybody know something about antiderivative solver online? Integral Calculator calculates an antiderivative (indefinite integral) of a function with respect to a given variable using analytical integration. The first thing is the antiderivative you will usually learn, when you begin your study of integral calculus.

As simple we can say, antiderivative finding is the exact opposite process of finding the derivative of any given function. So, before beginning a study of integral calculus, you must have a firm foundation in differential calculus. For an algebraic equation solver, antiderivative finding process is not very complex.

I hope the above explanation was useful. Keep reading and leave your comments.

Exterior of the triangle and Interior of the triangle

Hi Friends

Good Afternoon!!! In our previous blog we learned about Triangles. Now let us learn about "Exterior of the triangle and Interior of the triangle"

Interior of the triangle:

The region enclosed by the sides of a triangle is called the interior of the triangle.

In the figure, the points P, Q, R and X lie in the interior of QUOTE /\ABC.

Exterior of the triangle:

Any region outside the triangle is called the exterior of the triangle.

In the figure, points X, Y, Z and M lie in the exterior of /\ PQR.

I hope the above explanation was useful.

In our next blog we shall learn about 7 types of triangle. keep reading and leave your comments.

Factors of a number

Let Us Learn About Factors of a number

Consider the number 6, we have 6 divisible by 1, 2, 3, and 6.

Which means after division of 6 by any of 1, 2, 3, and 6, we get the remainder as zero.

These numbers 1, 2, 3, and 6 are called as factors of 6.

Factors of a number: factors of a number are those numbers which when divide the given number, leaves zero remainder.

Examples:

(i)3 and 5 are factors of 15 as 3x5 = 15

Also, 1x15 = 15

or, 1 and 15 are also factors of 15.

Thus, as we discussed above; 1, 3, 5 and 15 are factors of 15 as each of these numbers (1, 3, 5 and 15) divides number 15 exactly.

Let Us Learn On Methods Of Factorization

* Common Factor
* Prime Factor
* Highest Common Factor

Let Us understand About Common Factor
10 = 2 × 5 = 1 × 10

Thus, the factors of 10 are 1, 2, 5 and 10.
15 = 1 × 15 = 3 × 5
Thus, the factors of 15 are 1, 3, 5 and 15.
Clearly, 5 is a factor of both 10 and 15. It is said that 5 is a common factor of 10 and 15.

We shall Learn About Prime Factor in our next blog


Keep reading and leave your comments

Subtraction

Let Us Learn About Subtraction

First let us learn what is Subtraction.

Subtraction is the operation which finds the difference between the given two numbers. This is also one of the basic operations. There are two terms used in subtraction they are minuend and subtrahend. Where minuend is the term to be subtracted and subtrahend is the term which subtracts the minuend. When the value of the minuend is greatest then the result is positive. When the value of the subtrahend is greatest then the value is negative.

Subtraction Formula:

We shall learn on subtraction formula. The fixed names for the parts of the formula:

c − b = a

Are minuend(c) –subtrahend (b) = difference (a).

As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.

As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.

Let us understand with examples

The following problems are simple subtraction.

1) 9 - 9 = 0

The value 6 minus value 6 equal to 0

The solution is 0(zero).

2) 12 – 24 = - 12

The value 12 minus value 24 equal to minus 12

The solution is minus 12
3) 6 – 4 = 2

The value 6 minus value 4 equal to 2

The solution is 2

4) 10 – 7 = 3

The value 10 minus value 7 equal to 3

The solution is 3

5) 5.3 – 1.1 = 4.2

The decimal value 5.3 minus decimal value 1.1 equal to 4.2

The solution is 4.2(decimal value)

Keep readying and leave your comments.

Monomial

Let Us Learn About Monomial

A monomial is an algebraic expression in which the only operations that appear between the variables are the product and the power of the natural exponent.

2x²y³z

Parts of a Monomial

Coefficient

The coefficient of a monomial is the number that multiplies the variable(s).

Literal Part

The literal part is constituted by the letters and its exponents.

Degree

The degree of a monomial is the sum of all exponents of the letters or variables.

The degree of 2x² y³ z is: 2 + 3 + 1 = 6

Similar Monomials

Two monomials are similar when they have the same literal part.

2x² y³ z is similar to 5x² y³ z

Degree of a monomial:

The sum of the degrees/exponents of each of the variables in a monomial is called the degree of monomial.

Note: In a non-variable monomial, that is a constant which is any number other than zero, degree is always zero. Like 6, 3, 4, 2 etc. Have a degree zero!

• Degree of a Monomial: The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of xy is 2, the degree a^3 b of is 4, the degree of 12 is 0.
• Degree of a Polynomial: The degree of a polynomial is the greatest degree of any term in the polynomial. For example, the degree of x^5 - 5x^ 2 is 5, the degree of x^3+y^4-3x^2 = 2y is 4.

Solved Example on Degree

Find the degree of x^8y^6 + x^9 y^6.

Choices:

A. 8

B. 9

C. 16

D. 15

correct answer is d

Solution

Step 1: The degree of a polynomial is the greatest degree of any term in the polynomial.

Step 2: The degree of the second term in x^8y^6 + x^9 y^6 is ‘15’, which is the highest. So, the degree of the given polynomial is 15.

Related Terms for Degree

• Monomial
• Exponent
• Polynomial
• Variable
• Sum

• The degree of a monomial is the sum of the degrees in each of its variables.
• The degree of monomial is the sum of the exponents of the variable in the monomial.
• The degree of a nonzero constant term is 0.
  
• The constant 0 does not have a degree.

Example: Find the degree of monomial x⁷y³z².

Solution: Sum of the degree of in each variables is = 7+3+2 = 12.

Therefore the degree of the monomial is 12.

In our next we shall learn about degree of a polynomial