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Category: Maths

  • A number divisible by 8

    Divisibility by 8

    Divisibility Rule for 8

    ✅ Shortcut: Check the last 3 digits of the number. If those digits form a number divisible by 8, then the whole number is divisible by 8.

    Examples:

    Number Last 3 Digits Divisible by 8? Reason
    5816 816 ✅ Yes 816 ÷ 8 = 102
    2540 540 ❌ No 540 ÷ 8 = 67.5
    1000 000 ✅ Yes 0 is divisible by 8
    7512 512 ✅ Yes 512 ÷ 8 = 64
    3725 725 ❌ No 725 ÷ 8 = 90.625

  • A number divisible by 7

    Divisibility by 7

    Divisibility Rule for 7

    ✅ Shortcut: Take the last digit, double it, subtract from the rest. If the result is divisible by 7, so is the original number.

    Examples:

    Number Step Result Divisible by 7?
    203 20 − (2×3) 14 ✅ Yes
    301 30 − (2×1) 28 ✅ Yes
    259 25 − (2×9) 7 ✅ Yes
    321 32 − (2×1) 30 ❌ No
    161 16 − (2×1) 14 ✅ Yes

  • A number divisible by 6

    Divisibility by 6

    Divisibility Rule for 6

    ✅ A number is divisible by 6 if it is divisible by both 2 and 3.

    Examples:

    Number Divisible by 2? Divisible by 3? Divisible by 6? Reason
    12 ✅ Yes ✅ Yes ✅ Yes Both 2 & 3
    18 ✅ Yes ✅ Yes ✅ Yes Both 2 & 3
    20 ✅ Yes ❌ No ❌ No Only divisible by 2
    27 ❌ No ✅ Yes ❌ No Only divisible by 3
    30 ✅ Yes ✅ Yes ✅ Yes Both 2 & 3

  • A number divisible by 5

    Divisibility by 5

    Divisibility Rule for 5

    ✅ A number is divisible by 5 if the last digit is 0 or 5.

    Examples:

    Number Last Digit Divisible by 5? Reason
    25 5 ✅ Yes Ends in 5
    40 0 ✅ Yes Ends in 0
    73 3 ❌ No Ends in 3
    100 0 ✅ Yes Ends in 0
    91 1 ❌ No Ends in 1

  • A number divisible by 4

    Divisibility by 4

    Divisibility Rule for 4

    ✅ A number is divisible by 4 if the last two digits form a number divisible by 4.

    Examples:

    Number Last Two Digits Divisible by 4? Reason
    124 24 ✅ Yes 24 ÷ 4 = 6
    316 16 ✅ Yes 16 ÷ 4 = 4
    157 57 ❌ No 57 ÷ 4 = 14.25
    200 00 ✅ Yes 0 is divisible by 4
    718 18 ❌ No 18 ÷ 4 = 4.5

  • A number divisible by 3

    Divisibility by 3

    Divisibility Rule for 3

    ✅ A number is divisible by 3 if the sum of its digits is divisible by 3.

    Examples:

    Number Sum of Digits Divisible by 3? Reason
    123 1 + 2 + 3 = 6 ✅ Yes 6 is divisible by 3
    345 3 + 4 + 5 = 12 ✅ Yes 12 is divisible by 3
    127 1 + 2 + 7 = 10 ❌ No 10 is not divisible by 3
    81 8 + 1 = 9 ✅ Yes 9 is divisible by 3
    100 1 + 0 + 0 = 1 ❌ No 1 is not divisible by 3

  • A number divisible by 2

    Divisibility by 2

    Divisibility Rule for 2

    ✅ A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

    Examples:

    Number Last Digit Divisible by 2? Reason
    12 2 ✅ Yes Ends in an even digit
    57 7 ❌ No Ends in an odd digit
    104 4 ✅ Yes Ends in an even digit
    839 9 ❌ No Ends in an odd digit
    60 0 ✅ Yes Ends in 0

  • Numbers

    Types of Numbers

    Types of Numbers

    1. Natural Numbers

    Numbers from 1 and go on: 1, 2, 3, 4, 5, …

    2. Whole Numbers

    Natural numbers plus 0: 0, 1, 2, 3, …

    3. Integers

    Positive, negative numbers and 0: … -3, -2, -1, 0, 1, 2, …

    4. Even Numbers

    End with 0, 2, 4, 6, 8: 2, 4, 6, 8, 10, …

    5. Odd Numbers

    End with 1, 3, 5, 7, 9: 1, 3, 5, 7, 9, …

    6. Prime Numbers

    Only 2 factors: 2, 3, 5, 7, 11, …

    7. Composite Numbers

    More than 2 factors: 4, 6, 8, 9, …

    8. Rational Numbers

    Can be written as fractions: 1/2, 3/4, 5/1

    9. Irrational Numbers

    Cannot be written as fractions: √2, π

    10. Decimal Numbers

    Contain a dot: 3.5, 2.75, …

    11. Roman Numbers

    Old-style: I, V, X, L, C

    Fun Facts: 0 is neither positive nor negative. 2 is the only even prime. Numbers go on forever (∞).