Question

Can you stop checking for factor pairs when you find a pair that repeats?Explain

Answer 1

Solution:

Consider numbers which are Squares,cubes, fourths, fifths of some natural numbers.

For example, Starting from squares of some natural number: 4,9,16,25,36,49,64......

and their factors , which are 4= 1 × 2×1×2

9=1×3×1×3

16=2×1×2×1×2×1×2×1

25=1×5×1×5

36=2×3×2×3

64=2×4×2×4

Now coming to cubic numbers

8= 1 ×2×1×2×1×2

27= 1×3×1×3×1×3

3125= 3 ×5×3×5×3×5

So,the numbers whose factor pairs repeats are square, cubic, fourth,Fifth ,Sixth and.....higher powers of natural Numbers.

→→→So, we just need to check that whether those numbers whose factor pairs repeats are Squares, cubes or higher powers of natural numbers.