Mathematics: Prime, HCF, LCM, and Numbers

Prime Numbers

• A prime number is a whole number greater than 1 that is only divisible by 1 and itself.
• Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Highest Common Factor

• The highest common factor (HCF) is the largest number that divides two or more numbers exactly.
• To find the HCF, you can use prime factorization.

Lowest Common Multiple

• The lowest common multiple (LCM) is the smallest number that is a multiple of two or more numbers.
• To find the LCM, you can use prime factorization.

Square Numbers

• A square number is the result of multiplying a whole number by itself.
• For example, 9 is a square number because 3 x 3 = 9.
• The symbol for squaring a number is the superscript 2, so 3² = 9.

Cube Numbers

• A cube number is the result of multiplying a whole number by itself three times.
• For example, 27 is a cube number because 3 x 3 x 3 = 27.
• The symbol for cubing a number is the superscript 3, so 3³ = 27.

Square and Cube Roots

• The square root of a number is the number that, when multiplied by itself, equals the original number.
• For example, the square root of 9 is 3, because 3 x 3 = 9.
• The symbol for a square root is √.
• The cube root of a number is the number that, when multiplied by itself three times, equals the original number.
• For example, the cube root of 27 is 3, because 3 x 3 x 3 = 27.
• The symbol for a cube root is ³√.

Arithmetic Sequences

• An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.
• This constant difference is called the common difference.
• For example, 2, 5, 8, 11, 14 is an arithmetic sequence with a common difference of 3.

Other Sequences

• Other sequences include square, cube, and triangular numbers.
• Square numbers are formed by squaring consecutive whole numbers.
• Cube numbers are formed by cubing consecutive whole numbers.
• Triangular numbers are formed by adding consecutive whole numbers.

Adding and Subtracting Decimals

• When adding or subtracting decimals, make sure the decimal points are lined up.
• Add or subtract the numbers as usual, carrying over when necessary.

Multiplying Decimals

• When multiplying decimals, multiply the numbers as usual, ignoring the decimal points.
• Then count the total number of decimal places in the original numbers and place the decimal point in the answer that many places from the right.

Dividing Decimals

• When dividing decimals, divide the numbers as usual.
• If the divisor (the number you are dividing by) is a decimal, move the decimal point to the right until it is a whole number.
• Move the decimal point in the dividend (the number being divided) the same number of places to the right.
• Then divide as usual.

BIDMAS

• BIDMAS stands for Brackets, Indices (or Orders), Division and Multiplication (done from left to right), Addition and Subtraction (done from left to right).
• BIDMAS is a rule that tells you the order to perform operations in a mathematical expression.