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  • A number divisible by 11

    Divisibility by 11

    Divisibility Rule for 11

    ✅ Shortcut: Find the alternating sum of the digits. If the result is divisible by 11 (or equals 0), then the number is divisible by 11.

    Steps:

    • Take the digits of the number.
    • Alternately add and subtract them.
    • If the result is divisible by 11 or is 0, it’s divisible by 11.

    Examples:

    Number Alternating Sum Result Divisible by 11?
    2728 2 − 7 + 2 − 8 -11 ✅ Yes
    121 1 − 2 + 1 0 ✅ Yes
    1234 1 − 2 + 3 − 4 -2 ❌ No
    462 4 − 6 + 2 0 ✅ Yes
    713 7 − 1 + 3 9 ❌ No

  • A number divisible by 10

    Divisibility by 10

    Divisibility Rule for 10

    ✅ Shortcut: If a number ends in 0, it is divisible by 10.

    Examples:

    Number Last Digit Divisible by 10? Reason
    120 0 ✅ Yes Ends in 0
    3050 0 ✅ Yes Ends in 0
    67 7 ❌ No Does not end in 0
    890 0 ✅ Yes Ends in 0
    743 3 ❌ No Does not end in 0

  • A number divisible by 9

    Divisibility by 9

    Divisibility Rule for 9

    ✅ Shortcut: Add all the digits of the number. If the total is divisible by 9, then the whole number is divisible by 9.

    Examples:

    Number Sum of Digits Divisible by 9? Reason
    729 7 + 2 + 9 = 18 ✅ Yes 18 ÷ 9 = 2
    123 1 + 2 + 3 = 6 ❌ No 6 ÷ 9 = 0.666
    9999 9 + 9 + 9 + 9 = 36 ✅ Yes 36 ÷ 9 = 4
    2527 2 + 5 + 2 + 7 = 16 ❌ No 16 ÷ 9 = 1.77
    8019 8 + 0 + 1 + 9 = 18 ✅ Yes 18 ÷ 9 = 2

  • 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