Question

the sum of two numbers is 670 and their Hcf is 67. how many pairs of such numbers are valid? please answer as soon as possible!

Answer 1

Heya..

Suppose, these two numbers are (67a) and (67b); where a and b are integers and

67*(a + b) = 670

so, (a + b) = 10

Moreover, HCF (67a, 67b) = 67 = (67*1)

Therefore, a and b should be such chosen that HCF (a, b) = 1.

Such possible pairs of (a, b) are:

(1, 9) and (3, 7).

Therefore, the answer will be 2 pairs;

i) 67*1 = 67 & 67*9 = 603.

ii) 67*3 = 201 & 67*7 = 469.

Answer 2

Hey mate ^_^

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Answer:
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Two numbers are (67a) and (67b); where a and b are integers.

67 × (a + b) = 670

So,

(a + b) = 10

HCF (67a, 67b) = 67 = (67 × 1)

Therefore,

a and b should be such chosen that HCF (a, b) = 1

Such possible pairs of (a, b) are: (1, 9) and (3, 7)

Final answer:

=> 67 × 1 = 67 & 67 × 9 = 603
=> 67 × 3 = 201 & 67 × 7 = 469

#Be Brainl❤️