Video: Finding the Next Two Even Numbers after a Given Number

The smallest of three consecutive even numbers is 598. What are the other two?

02:24

Video Transcript

The smallest of three consecutive even numbers is 598. What are the other two?

Before we start thinking about the numbers involved, let’s remind ourselves what the word consecutive means. It might be a long word, but it just means one after another. So if we’re thinking about three consecutive numbers, we’re thinking about three numbers that come one after the other. They belong next door to each other on a number line. We’re told that the smallest of three consecutive even numbers is 598. This means that the other two numbers we’re looking for are going to be greater than 598. 598 is the smallest of the three. So surely this just means that we should count on from 598.

The next number that comes after it would be 599. And the number after that is 600. So have we found our other two numbers? Well, if we think this, then we need to read our question more carefully. There’s a word in the question that we haven’t thought about. We’re told that the smallest of three consecutive even numbers is 598. Now, consecutive even numbers must be even numbers that come one after another. We know that an even number contains a two, a four, a six, an eight, or a zero in the one’s place. That’s how we know 598 is an even number. It has eight ones.

599 is an odd number because nine is an odd digit, so we can forget 599. But the next consecutive even number after 598 is 600. 600 contains zero ones. After 600 comes 601, which we can forget about because this is an odd number, and then comes 602, which we know is an even number. So the way to find consecutive even numbers is simply to count in twos. 598, 600, 602. If the smallest of three consecutive even numbers is 598, the other two numbers are 600 and 602.

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