Question Video: Finding the Largest/Least 𝑛-Digit Multiple of a Number

Find the largest 6-digit multiple of 5.

03:19

Video Transcript

Find the largest six-digit multiple of five.

To help us solve this problem, let’s use a place value grid to think about the value of each digit in a six-digit number. The smallest value digit is worth ones. The next place is worth tens. Then we have hundreds, thousands. The digit to the left of the thousands digit is worth ten thousands. And the final digit in our six-digit number has a value of hundred thousands. Now, the question asks us to find the largest six-digit multiple of five.

What do we know about the multiples of five? These are numbers that we find by multiplying another number by five. They’re numbers in the five times table. And if we think about the numbers in the five times table, we can spot a pattern that will help us to identify multiples of five. Five, 10, 15, 20, 25, and so on. Can you see the pattern? Multiples of five always end in a five or a zero. Now, for our six-digit number to be a multiple of five, we’re either going to need to write a five in the ones place or a zero in the ones place. Which shall we choose?

Now, the problem asks us to find the largest six-digit multiple of five. Now, the digit five is larger than zero. So let’s write the largest possible digit that we can in the ones place. For it to be a multiple of five, we can only write five or zero. So we’ve chosen the larger of those two options. Now, how many ten should our number have? Well, to make the number as large as possible, we need to use the largest possible digit. We’ve already made sure that our number is going to be a multiple of five by using five in the ones place. So now, we just need to choose the largest possible digit every time. And the largest possible digit is nine. Our number needs to have nine tens and also nine hundreds, nine thousands, nine lots of ten thousand, and nine hundred thousands.

If we chose to use any digit other than all these nines, our number would be less. We want to make the largest possible six-digit multiple of five. So we have to use these large digits. The largest possible six-digit number is 999999. But we weren’t asked to make the largest possible six-digit number. We were asked to make the largest possible six-digit multiple of five. So to make sure our number was a multiple of five, we needed to use either a zero or a five in the ones place. Five is greater than zero, so five was the best digit to use. The largest six digit multiple of five is 999995.

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