{"id":3964,"date":"2021-11-17T15:48:37","date_gmt":"2021-11-17T15:48:37","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=3964"},"modified":"2022-01-02T07:27:03","modified_gmt":"2022-01-02T07:27:03","slug":"divisible-by-11-rules-examples-and-faq-mindspark","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/divisible-by-11-rules-examples-and-faq-mindspark\/","title":{"rendered":"Divisible By 11: Rules, Examples and FAQ – Mindspark"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Divisible By 11: Rules, Examples and FAQ – Mindspark<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

A number is divisible by 11 if it leaves zero as the remainder when divided by 11. Here we will understand the divisibility rule of 11 with some examples.<\/p>\n

 <\/p>\n

How to find if a number is divisible by 11?<\/h2>\n

The divisibility rule of 11 tells us if a number can be wholly divided by 11 without leaving any remainder.<\/p>\n

Usually, we check this by dividing the given number by 11. But the divisibility rule of 11 has a shortcut method to tell if a number is divisible by 11 or not.<\/p>\n

To apply this rule, we add the digits at odd and even places of the given number. Then we calculate the difference between both the results. If the difference is zero or a multiple of 11, we confirm that the given number is also divisible by the number 11. For finding the difference, we always subtract the smaller sum from the larger sum.<\/p>\n

Let us clear this with an example.<\/p>\n

Example –<\/strong> Let us apply the divisibility rule of 11 on the number 1331.
In the given number, digits at odd places = 1, 3 and digits at even places = 3, 1.
Sum of digits at odd places = 1 + 3 = 4 and sum of digits at even places = 3 + 1 = 4
Difference = 4-4 = 0
Since the difference obtained is zero, we can confirm that 1331 is divisible by the number 11.<\/p>\n

Now, let us do this operation on a large number, 162272.
In the given number,
Sum of digits at odd places = 1 + 2 + 7 = 10
Sum of digits at even places = 6 + 2 + 2 = 10
Difference = 10 – 10 = 0
Since the difference is 0, so the number 162272 is divisible by the number 11.<\/p>\n

 <\/p>\n

Examples<\/b><\/h2>\n

<\/b><\/p>\n

1. Using the divisibility rule of 11, check whether the number 25110 is divisible by 11?<\/strong><\/h3>\n

Ans:<\/strong><\/p>\n

Let us check if 25110 is divisible by the number 11 or not?<\/span><\/p>\n

Sum of digits at odd places = 2 + 1 + 0 = 3<\/span><\/p>\n

Sum of digits at even places = 5 + 1 = 6<\/span><\/p>\n

Difference = 6 – 3 = 3<\/span><\/p>\n

Since the difference is 3, which is not a multiple of 11, the number 25110 is not divisible by the number 11.<\/span><\/p>\n

<\/span><\/p>\n

<\/span><\/h3>\n

<\/span><\/h3>\n

2. Which number is divisible by 11? (a) 1510 (b) 1452 (c) 1010 (d) 1121<\/strong><\/h3>\n

Calculate the sum of the digits at odd places and even places of the number.\u00a0 If the sum difference is 0 or divisible by the number 11, the given number is divisible by 11. So, let\u2019s check each number one by one.<\/span><\/p>\n

a. 1510<\/span><\/p>\n

Difference between sum of digits at odd places and even places<\/span><\/p>\n

= (5 + 0) – (1 + 1) = 5 – 2 = 3<\/span><\/p>\n

Therefore, 1516 is not divisible by the number 11.\u00a0 <\/span><\/p>\n

b. 1452<\/span><\/p>\n

Difference between sum of digits at odd places and even places<\/span><\/p>\n

= (1 + 5) – (4 + 2) = 6 – 6 = 0<\/span><\/p>\n

Therefore, 1452 is divisible by the number 11.<\/span><\/p>\n

c. 1011<\/span><\/p>\n

Difference between sum of digits at odd places and even places<\/span><\/p>\n

= (1 + 1) – (0 + 1) = 2 – 1 = 1<\/span><\/p>\n

Therefore, 1010 is not divisible by the number 11.<\/span><\/p>\n

d. 1121<\/span><\/p>\n

Difference between sum of digits at odd places and even places<\/span><\/p>\n

= (1 + 2) – (1 + 1) = 3 – 2 = 1<\/span><\/p>\n

Therefore, 1121 is not divisible by the number 11.<\/span><\/p>\n

 <\/p>\n

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Explore Other Topics<\/h1>\n

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Related Concepts<\/h1>\n

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\n
Divisibility Rules<\/a><\/div>\n
<\/a>Divisibility rule of 7<\/a><\/div>\n
Divisibility rule of 13<\/a><\/a><\/div>\n<\/div>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    1. What is the Divisibility Rule of 11?<\/strong><\/h3>\n

    Ans: <\/strong>We add the digits at odd and even places of the given number. Then we calculate the difference between both the additions. If the difference is zero or a number divisible by the number 11, we confirm that the given number will also be completely divided by 11.
    <\/span><\/p>\n

    <\/span><\/p>\n

    <\/span><\/p>\n

    <\/span><\/h3>\n

    2. Which is the smallest and the largest 4-digit number divisible by 11?<\/strong><\/h3>\n

    Ans: <\/strong>1001 and 9999 are the smallest and the largest 4-digit numbers, respectively, divisible by the number 11. In 1001, the difference between the sum of the digits at odd and even places was (1 + 0) – (0 + 1), which is 0. Similarly, for 9999, the difference between the sum of the digits at odd and even places is\u00a0 0.\u00a0<\/span><\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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