IGCSE Math 0580 Numbers Glossary

igcse-maths-notes-glossary

 

0580 IGCSE Math Numbers Glossary

1. Natural Numbers:

  • Numbers that are used fro counting purpose are called as Natural Numbers. 
  • These numbers are a part of real numbers
  • These include all positive numbers from one to infinity
  • Example: 1,2,3,4...........

2. Whole Numbers:

  • All natural numbers along with a "zero" are called as whole numbers
  • They are a part of real numbers
  • They do not include fractions  or decimals
  • All natural numbers are included in the whole number group

3. Rational Numbers

  • These are the numbers that can be represented as the ratio of two integers
  • The denominator of rational numbers is never zero

4.Irrational Numbers:

  • These numbers are real numbers that cannot be expressed as fractions.
  • These numbers cannot be written as the ratio of two integers
  • Irrational numbers consist of non-terminating and non-recurring decimals. 

5.Terminating decimals:

  • This is a decimal that has an end
  • Example 36/8=4.5

6. Non-terminating decimals

  • Decimals  that do not have an end and repeat endlessly.
  • Examples: 0.54444444.....

7. Even Numbers:

  • Numbers that are completely divisible by 2 are called as even numbers
  • Even numbers end in 0,2,4,6 or 8

8. Odd Numbers:

  • Odd numbers are not completely divisible by 2
  • Odd numbers end in 1,3,5,7 or 9

9.Real Numbers:

  • These include rational as well as irrational numbers

10. Integer:

  • An integer is a whole number that can be positive, negative or zero.
  • It is never a fraction or a decimal

11. Prime number:

  • A prime number is a whole number greater than 1 and has only 2 factors, one and itself.

12. Square number:

  •  To get a square number, all you need to do is to multiply an integer ( which is not a fraction) by itself.
  • Example of a square number is 25, because 25 is obtained by multiplying 5 by itself.

13. Cube number

  • A number obtained by multiplying an integer by itself three times is called as a cube number.
  • Example 125 is a cube number because 125=5x5x5 [ or 125 is obtained by multiplying 5 by itself three times.]

14. Factors:

  • A factor is a number that divides another number leaving no remainder.
  • Example: 6 can be divided by 3, without leaving any remainder. So 3 and 2 are factors of 6

15. Multiples:

  • Consider two numbers, for example 3 and 6.When you multiply these two numbers , you get 18. Here 18 is called as the multiple

Revision Notes

0580 Maths Glossary:

The following Maths glossary for 0580 Maths is  perfectly aligned with the requirements of the mark scheme. It is valid for all exams for 2025/2025/2027, for both CORE and Extended Syllabus

C1.1 Types of Numbers

  • Natural Numbers: Numbers used for counting (e.g., 1, 2, 3, ...). Example: 5 is a natural number.
  • Integers: Numbers that can be positive, negative, or zero (e.g., -3, 0, 7). Example: -10 is an integer.
  • Prime Numbers: Numbers greater than 1 that have exactly two factors: 1 and itself (e.g., 2, 3, 5, 7). Example: 13 is a prime number.
  • Square Numbers: Numbers obtained by squaring integers (e.g., 1, 4, 9, 16). Example:  52 = 25 
  • Cube Numbers: Numbers obtained by cubing integers (e.g., 1, 8, 27, 64). Example:  33 = 27 
  • Common Factors: Factors shared by two or more numbers. Example: Common factors of 12 and 18 are 1, 2, 3, and 6.
  • Common Multiples: Multiples shared by two or more numbers. Example: Common multiples of 4 and 6 are 12, 24, 36, etc.
  • Rational Numbers:Numbers that can be expressed as fractions, 1/2, -3, 0.75. Example: 7/4 is a rational number.
  • Irrational Numbers: Numbers that cannot be expressed as fractions Example: e.g., ?, ?2. Example: ?3 is an irrational number.
  • Reciprocals: A reciprocal of a number is 1 divided by that number. Example: The reciprocal of 5 is 1/5.

Example Tasks

  • Convert Numbers and Words:
    • Six billion is 6000000000.
    • 10007 is ten thousand and seven.
  • Prime Factorization: Express 72 as a product of its prime factors: 72 = 23  x  32

 

Methods:

Prime Factorization: Express 727272 as a product of its prime factors

  1. Start dividing by the smallest prime number, 222, until you can't divide further:

    • 72÷2=36
    • 72÷2=36
    • 36÷2=18
    • 18÷2=9

  2. Switch to the next smallest prime, 3:

    • 9÷3=3
    • 3÷3=1

  3. Write 72 as a product of primes:
    72=23×32

  • Find HCF: The highest common factor (HCF) of 24 and 36 is 12.

Method:

 

  • Perform prime factorization:

    • 24= 23 x 3
    • 36= 22 x 32

  • Identify the common prime factors with the lowest powers:

    • Common factors: 22 and 3

  • Multiply these common factors:
    HCF=22×3=4×3=12

  • Find LCM: The lowest common multiple (LCM) of 4 and 6 is 12.

???????Method:

 

  • Perform prime factorization:

    • 4=22
    • 6=2×3

  • Take all prime factors, using the highest powers:

    • From 4: 22
    • From 6: 3

  • Multiply these factors:
    LCM+22×3=4×3=12

The LCM of 4 and 6 is 12. To find the least common multiple (LCM) of 4 and 6, we need to find the multiples of 4 and 6 (multiples of 4 = 4, 8, 12, 16; multiples of 6 = 6, 12, 18, 24) and choose the smallest multiple that is exactly divisible by 4 and 6, i.e., 12.

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