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Write 825 as a product of its prime factors.

Prime factors are numbers that can only be fully divided by itself and 1.

For example, 2, 3 and 5 are prime numbers since they can only be divided by itself and 1. However, 6 is not a prime number because it can also be divided by 2 and 3.

Is it easy to see that 825 can be divided by 5 (a prime number). Doing this gives us 165.

Once again, 165 can be divided by 5! The result is 33.

33 can be divided by 3, giving us a quotient of 11.

11 can not be divided by any integer other than itself and 1, and so is a prime number in itself.

Therefore, 825 can be expressed as 11*5*5*3 or, in a simplified format, 11 * 5^2 * 3

Ewan V. GCSE Maths tutor, A Level Maths tutor

9 months ago

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