Editing Extended Euclidean algorithm (section)

=== Example ===

The following table shows how the extended Euclidean algorithm proceeds with input {{nowrap|{{green|240}}}} and {{nowrap|{{green|46}}}}. The greatest common divisor is the last non zero entry, {{nowrap|{{red|2}}}} in the column "remainder". The computation stops at row 6, because the remainder in it is {{nowrap|{{red|0}}}}. Bézout coefficients appear in the last two columns of the second-to-last row. In fact, it is easy to verify that {{nowrap|1={{magenta|−9}} × {{green|240}} + {{magenta|47}} × {{green|46}} = {{red|2}}}}. Finally the last two entries  {{nowrap|{{cyan|23}}}} and {{nowrap|{{cyan|−120}}}} of the last row are, up to the sign, the quotients of the input {{nowrap|{{green|46}}}} and {{nowrap|{{green|240}}}} by the greatest common divisor {{nowrap|{{red|2}}}}.

{| class="wikitable" style="text-align:right;"
! index ''i''!! {{blue|quotient ''q''<sub>''i''−1</sub> }}!! {{olive|Remainder ''r''<sub>''i''</sub>}}!! {{brown|''s''<sub>''i''</sub> }}!! ''t''<sub>''i''</sub>
|-
| 0 || ||{{green|240}}||{{brown|1}} || 0
|-
| 1 || 
||{{green|46}} || {{brown|0}} || 1
|-
| 2 ||{{green|240}} ÷ {{green|46}} = {{blue|5}}
||{{green|240}} − {{blue|5}} × {{green|46}} = {{olive|10}}
||{{brown|1}} − {{blue|5}} × {{brown|0}} = {{brown|1}}
|| 0 − {{blue|5}} × 1 = −5
|-
| 3 ||{{green|46}} ÷ {{olive|10}} = {{blue|4}}
||{{green|46}} − {{blue|4}} × {{olive|10}} = {{olive|6}}
||{{brown|0}} − {{blue|4}} × {{brown|1}} = {{brown|−4}}
|| 1 − {{blue|4}} × −5 = 21
|-
| 4 ||{{olive|10}} ÷ {{olive|6}} = {{blue|1}}
||{{olive|10}} − {{blue|1}} × {{olive|6}} = {{olive|4}}
||{{brown|1}} − {{blue|1}} × {{brown|−4}} = {{brown|5}}
|| −5 − {{blue|1}} × 21 = −26
|-
| 5 ||{{olive|6}} ÷ {{olive|4}} = {{blue|1}}
||{{olive|6}} − {{blue|1}} × {{olive|4}} = {{red|2}}
||{{brown|−4}} − {{blue|1}} × {{brown|5}} = {{magenta|−9}}
|| 21 − {{blue|1}} × −26 = {{magenta|47}}
|-
| 6 ||{{olive|4}} ÷ {{olive|2}} = {{blue|2}}
||{{olive|4}} − {{blue|2}} × {{olive|2}} = {{red|0}}
||{{brown|5}} − {{blue|2}} × {{brown|−9}} = {{cyan|23}}
|| −26 − {{blue|2}} × 47 = {{cyan|−120}}
|}