Question

The numbers 630 and 1248, written as the products
of their prime factors, are 630 = 2 x 32 x 5 x 7 and
1248 = 25 x 3 x 13. Find
(i) the smallest non-zero whole number n for which 630n is a multiple of 1248,

(ii) the smallest whole number m for which 1248/m is a factor of 630.
​

Answer 1

Answer:

(i) n=5*13=65

(ii)m=3*2*7=42

Step-by-step explanation:

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Answer 2

The answers are

The answers are (i) n = 208

The answers are (i) n = 208 (ii) m = 208

GIVEN

The numbers 630 and 1248, written as the products

of their prime factors, are 630 = 2 x 32 x 5 x 7 and

1248 = 25 x 3 x 13.

TO FIND

(i) the smallest non-zero whole number n for which 630n is a multiple of 1248,

(ii) the smallest whole number m for which 1248/m is a factor of 630.

SOLUTION

The above problem can be simply solved as follows;

(i)

Let 630n is a multiple of 1248

Prime factors of 630n = 2 × 3² × 5 × 7 × n

= 2⁵ × 3² × 5 × 7 × 13

n = 2⁴ × 13 = 208

(ii)

If,

1248/m is a factor of 630

1248/m = (2⁵ × 3 × 13)/m = 2 × 3

m = 2⁴ × 13 = 208

Hence, The answers are

Hence, The answers are (i) n = 208

Hence, The answers are (i) n = 208 (ii) m = 208

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