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.

Test your knowledge on prime numbers, highest common factors, lowest common multiples, square numbers, and cube numbers. This quiz covers essential concepts and examples that form the foundation of number theory. Perfect for students looking to solidify their understanding of these mathematical principles.