Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 3 • Question 7

Write down a square number whose digits sum to a prime number.

02:09

Video Transcript

Write down a square number whose digits sum to a prime number.

We have two definitions that we need to be aware of in this question, a square number and a prime number. A square number is the product of a number multiplied by itself. The first five square numbers are one, four, nine, 16, and 25. One multiplied by one is equal to one. Two multiplied by two is equal to four. Three multiplied by three is equal to nine and so on.

A prime number is a number that has exactly two factors, one and itself. A prime number will not be divisible by any number apart from one and itself. The first five prime numbers are two, three, five, seven, and 11. The only factors of two are one and two. The only factors of three are one and three. The only factors of five are one and five and so on.

We were asked to write down a square number whose digits sum or add to a prime number. We can immediately rule out the first three square numbers as none of one, four, and nine are prime. The digits of the square number 16 are one and six. One plus six is equal to seven. And seven is indeed a prime number as its only factors are one and seven.

This means that a correct answer for a square number whose digits sum to a prime number is 16. Other examples of correct answers here are 25 and 49. The digits two and five sum to seven. And the digits four and nine sum to 13. Both of these are prime numbers.

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