Question

Express each of the following numbers as a product of Prime factors:
a. 500
b. 1372
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Answer 1

Solution

500 = 5 x 5 x 5x2x2

* In the above prime factorisation 2 x2 remain after grouping the prime factors in

triples.

5/ 500

5/100

5/20

2/4

5/2

/1

We have 1372 = 2 x 2 x 7 x 7 x7

Since, the prime factor 2 does not appear in a group of triples.

21372

2686

7343

749

77

1

.. 1372 is not a perfect cube.

Obviously, to make it a perfect cube we need one

more 2 as its factor.

i.e.

or

[1372] x 2 = [2 x 2x7x7x7] x2

2744 = 2 x 2 x2x7x7x7

which is a perfect cube.

Thus, the required smallest number = 2.

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