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The Consecutive Even Numbers Brain Teaser
Two consecutive positive even numbers multiply together to make 288. What are the two numbers?
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What's the puzzle?
Two consecutive positive even numbers multiply together to make 288. What are the two numbers?
What's the answer?
16 and 18
How do you work it out?
- Call the smaller number n. The next even number is n + 2.
- Their product is n(n + 2) = 288, so n² + 2n - 288 = 0.
- Factorise: (n + 18)(n - 16) = 0, so n = 16 or n = -18.
- The numbers must be positive, so n = 16 and the next even number is 18.
- The numbers are 16 and 18. Check: 16 × 18 = 288.
Frequently asked questions
How do you write consecutive even numbers in algebra?
Consecutive even numbers go up in twos, so if the first is n the next is n + 2. In the consecutive even numbers puzzle this gives the equation n(n + 2) = 288, which rearranges to a quadratic.
Is there a quick way to check the consecutive even numbers puzzle?
Yes. Two numbers close together multiply to roughly the square of their midpoint, and 17 × 17 = 289, so the numbers sit either side of 17. LoveMaths Tutoring UK uses this estimate to check the algebra.
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