Important Formulae: Numbers | Mathematics & Pedagogy Paper 1 for CTET & TET Exams - CTET & State TET PDF Download

A prime number has exactly two distinct positive divisors: 1 and itself.

Examples: 2, 3, 5, 7, 11, 13, ...

Even Numbers

A number is even if it is divisible by 2 without a remainder.

Examples: 2, 4, 6, 8, 10, ...

Odd Numbers

A number is odd if it is not divisible by 2 evenly.

Examples: 1, 3, 5, 7, 9, ...

Factors of a Number

Factors are the numbers you multiply together to get another number.

Example: Factors of 12 are 1, 2, 3, 4, 6, and 12.

Least Common Multiple (LCM)

LCM of two or more numbers is the smallest number that is a multiple of each of them.

Example: LCM of 4 and 6 is 12.

Greatest Common Divisor (GCD)

GCD of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Example: GCD of 8 and 12 is 4.

Place Value

The place value of a digit in a number is the value it holds in that number.

Example: In 342, the place value of 4 is hundreds, which is 400.

Face Value

The face value of a digit in a number is the digit itself, regardless of its place value.

Example: In 342, the face value of 4 is 4.

Number Line

A number line is a line on which numbers are marked at intervals, used to visualize number order and relationships.

Example: A number line for integers could be: ... -3, -2, -1, 0, 1, 2, 3, ...

Ascending Order

Arranging numbers from smallest to largest.

Example: 5, 7, 9, 12, 15 in ascending order.

Descending Order

Arranging numbers from largest to smallest.

Example: 20, 18, 15, 11, 9 in descending order.

Rounding Numbers

Rounding a number means replacing it with a nearby number that is easier to work with or remember.

Example: Rounding 12,345 to the nearest thousand gives 12,000.

Roman Numerals

A numeral system originating in ancient Rome, where numbers are represented by combinations of letters from the Latin alphabet.

Example: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

Factorial

The product of all positive integers up to a given number.

Example: 5! = 5 × 4 × 3 × 2 × 1 = 120.

Percentage

A proportion or rate per hundred.

Example: 20% means 20 out of 100.

Average or Mean

The sum of a set of numbers divided by how many numbers are in that set.

Example: Average of 2, 4, 6 is (2 + 4 + 6) / 3 = 4.

Arithmetic Progression (AP)

A sequence of numbers in which the difference between consecutive terms is constant.

Example: 1, 3, 5, 7, 9 is an AP with a common difference of 2.

Geometric Progression (GP)

A sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Example: 2, 6, 18, 54 is a GP with a common ratio of 3.