Factors of a number

• When two or more numbers are multiplied together to get the product, each number is called a factor of the product.
• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• 5 cannot be multiplied by any other number to get the product 12, therefore 5 is not a factor of 12.

Finding all factors of 16

• 1 x 16 = 16
• 2 x 8 = 16
• 4 x 4 = 16
• 8 x 2 = 16
• 16 x 1 = 16
• 1, 2, 4, 8, and 16 are factors of 16.

Finding all factors of 27

• 1 x 27 = 27
• 3 x 9 = 27
• 9 x 3 = 27
• 27 x 1 = 27
• 1, 3, 9, and 27 are factors of 27.
• When a number is divided by its factor, it leaves no remainder.

Finding two factors of 18 using division

• 18 ÷ 2 = 9, remainder = 0
• 2 and 9 are factors of 18.

Finding two factors of 27 using division

• 27 ÷ 3 = 9, remainder = 0
• 3 and 9 are factors of 27
• 27 ÷ 2 = 13, remainder = 1
• 2 is not a factor of 27.

Finding two factors of 35 using division

• 35 ÷ 5 = 7, remainder = 0
• 7 and 5 are factors of 35
• 35 ÷ 2 = 17, remainder = 1
• 35 ÷ 3 = 11, remainder = 2
• 35 ÷ 4 = 8, remainder = 3
• 2, 3, and 4 are not factors of 35.

Facts about factors

• A factor of a number will always be smaller than or equal to the number.
• The factors of 6 are 1, 2, 3, and 6.
• 1 and the number itself are factors of any number.
• The factors of 14 are 1, 2, 7, and 14.
• The number 1 has only one factor: the number 1.
• All other numbers will have at least two factors.
• Division of a number by any of its factors leaves no remainder.

Finding factors by multiplication

• Find the numbers that can be multiplied with any other number to give the required product.

Factors of 20

• 1 x 20 = 20
• 2 x 10 = 20
• 3 x ?
• 4 x 5 = 20
• 5 x 4 = 20
• 6 x ?
• 1, 2, 4, 5, 10, and 20 can form the product 20, therefore they are all factors of 20.
• 3 cannot be multiplied with any number to give 20, therefore 3 is not a factor of 20.

Finding factors by division

• Find the divisors from 1 till n (number) that can divide n (number) without leaving a remainder.

Factors of 18

• 18 ÷ 1 = 18, R = 0
• 18 ÷ 2 = 9, R = 0
• 18 ÷ 3 = 6, R = 0
• 18 ÷ 4 = 4, R = 2
• 1, 2, 3, 6, 9, and 18 divide 18 without leaving a remainder, therefore they are all factors of 18.
• Division of 18 by 4 leaves a remainder of 2, therefore 4 is not a factor of 18.
• The divisor is not only the factor, if it leaves no remainder, the quotient is also a factor of the number.

Determining if a number is a factor of another number

• A smaller number will be a factor of another number if the division by that number leaves 0 as the remainder.

Example 1: Is 5 a factor of 95?

• 95 ÷ 5 = 19, remainder = 0
• The remainder is 0, therefore 5 is a factor of 95.

Example 2: Is 3 a factor of 17?

• 17 ÷ 3 = 5, remainder = 2
• 17 ÷ 3 leaves 2 as the remainder, therefore 3 is not a factor of 17.

Prime and composite numbers

• Prime numbers are numbers that have only two factors: 1 and the number itself.
• Numbers that have more than two factors are called composite numbers.
• The number 1 is neither prime nor composite, it is a unique number that has only 1 factor.

Prime factorization

• Writing a number as a product of its factors is called factorization.
• Writing a number as a product of its prime factors only is called prime factorization.
• There are two methods to find the prime factors of a number: Factor tree method and Short division method.

Factor Tree Method

• Factorise the numbers in such a way that at least one of the factors is a prime factor.
• Then factorise the composite factor further to get at least one prime factor.
• Continue this way until all the factors are prime factors.

Short Division Method

• Write n (number) as the dividend.
• Divide it by the smallest prime factor.
• If the new dividend is not divisible by 2, move on to the next prime number 3.
• Continue this way until the quotient is 1.
• Prime factorization = Product of the prime number of divisors

Common factors

• While observing the factors of two or more numbers, some of the factors may be the same, and are known as common factors.

Twin Primes

• Prime numbers 3 and 5 have a composite number in between, and such prime numbers are called twin primes.

Consecutive Prime Numbers

• Prime numbers 2 and 3 come one after the other, and are called consecutive prime numbers.

Multiples

• A multiple contains many more units of the number (n).
• There can be many other multiples of n (number).
• Number of multiples are unlimited.
• To find the 4th multiple of 3, make four jumps of 3 each.

Facts about Multiples

• Each number is a multiple of itself.
• Every number is a multiple of 1. The first multiple of a number is the is the number itself.
• A multiple is a product of two numbers, and the product is a multiple of each of these two numbers.
• Multiples of any number are countless, there is no last multiple of a number.

Finding Multiples

• We can get the multiples by simply multiplying it number with natural numbers, 1, 2, 3, 4 and so on.

Finding out if one number is a multiple of the other

• If there is no remainder, the bigger number is a multiple of the smaller number.

Common Multiples

• Common multiples are the multiples which are common for two or more numbers.

Test of Divisibility

• The rules enable us to find out if one number is divisible by another, without carrying out the actual division.

Test of Divisibility by 2

• A number is divisible by 2 if it does not leave any remainder when divided by 2.
• A number is divisible by 2 if its ones place is divisible by 2.
• A number is divisible by 2 if it has 0, 2, 4, 6, or 8 in its ones place.

Simple Closed Curves Types

• Made of the line segment only
• Made of curved lines only
• Made of both line segments and curved lines

Polygons

• An enclosed figure made of three or more line segments is called a polygon.
• The line segments of a polygon are known as its sides.
• The meeting point of two line segments is called a corner or vertex.
• Polygon gets its name from number of sides it has

Kinds of Polygons

• 3 sides : Triangle
• 4 sides : Quadrilateral
• 5 sides : Pentagon
• 6 sides : Hexagon

Point, Line, Line Segment, and Ray

• A point is a position on a plane surface which denoted by capital letter.
• A line is straight path and length can not be measured
• A line segment that is between two end points and length has fixed.
• A ray is part of a line, has one end point, it extends one direction without ending.
• A triangle has 3 vertices and 3 sides
• A quadrilateral has four sides and four vertices.
• The curved line in the circle is the boundary or outer edge
• A line drawn from the center to any point on the circumference of the circle is called the radius.
• The diameter passes through the center and joins two points on the circumference of the circle.

Types of triangles

• Scalene triangle: A triangle with three unequal sides
• Isosceles triangle: A triangle with two equal sides
• Equilateral triangle: With three equal sides is called an equilateral triangle
• The distance from the centre to any point on the circumference of the circle is called its radius.
• Length of boundary on the circle is called its circumference.

Diameter and radius of a circle

• The radius was half its diameter of the circle

Symmetry and mirror reflection

• A figure that can be divided into halves such that the two halves match exactly is called a symmetrical figure.
• Some shapes have more than one line of symmetry.
• The dotted line along the middle is the line of symmetry which called reflection symmetry .

Tessellations

• A repeating pattern of shapes that fit perfectly together, with no overlaps or gaps, is known as tessellation.
• Tessellations can be created by repeating some polygons.

Equivalent Fractions

• Equivalent fractions are fractions that have the same value, even though they may look different.
• To find the equivalent fractions of a given fraction, multiple or devide the numerator and denomination with the same number

Like Fractions

• Fractions with the same denominators are called like fractions.

Unlike Fractions

• Fractions with different denominators are called unlike fractions.

Comparision of Like Fractions

• When comparing two or more fractions with the same denominators, the larger fraction is the one with the greater numerator because the whole is divided into the same number of parts in each of them.

Decimals

• A decimal is a way of writing a number that is not 'whole'. Put another way, these are in-between numbers.
• The numbers written on the right side of a decimal point are parts of whole numbers, called decimal places.

To Find Fraction of a number

• Multiply the numerator of the fraction with the number.
• Then, divide the product by the denominator of the fraction.

Reducing Fractions

• Reducing a fraction means making the fraction as simple as possible, and can be done by dividing both its numerator and denominator by a common factor.

Types of Fractions

• A fraction where the numerator is smaller than the denominator is called a proper fraction.
• A fraction where the numerator is greater than or equal to the denominator is called an improper fraction.
• A fraction that is maade of a whole number and a proper fraction is called mixed fraction

Mixed fractions can be made into improper fractions using these steps

• Find the product of the whole number and the denominator.
• Add the numerator to the product and treat it as the numerator of the improper fractions
• Retain the denominator

Perimeter

• Perimeter is defined as the length of the boundary of any shape and find the perimeter, we just add the lengths of the sides along the boundary