Question Video: Finding the Largest Number Formed from a Given Set of Digits That Is Divisible by a Given Number

Find the largest number formed from 5, 6, 7 and 8 which is divisible by 5.

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Video Transcript

Find the largest number formed from five, six, seven, and eight which is divisible by five.

As there are four digits, our number will have a number in the thousands column, the hundreds column, the tens column, and the units column. Placing the numbers in ascending order, 5678, gives us the smallest possible number from these four digits. Placing them in descending order, 8765, gives us the largest possible number. Any whole number or integer is divisible by five, if its units digit is five or zero. We have already worked out that the largest possible number is 8765. The units digit of this number is five. Therefore, it will be divisible by five. The largest number formed from the digits five, six, seven, and eight which is divisible by five is 8765.

We can check that this number is divisible by five by using our bus stop method. Eight divided by five is equal to one remainder three. We need to carry the three to the hundreds column. 37 divided by five is equal to seven remainder two. 26 divided by five is equal to five remainder one. Finally, 15 divided by five is equal to three. 8765 divided by five is equal to 1753. We have, therefore, confirmed that it is divisible by five.

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