Question

find the the largest number which exactly divides 418and 1866 and leaving reminder 4 and 3 respectively
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Answer 1

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Answer 2

Answer:

207 is the largest number which divides 418 and 1866 and leaving behind a reminder of 4 and 3 respectively.

Step-by-step explanation:

Now,

If we think logical, remainder value is just the subtraction of the dividend by a number,

So let the number be x

then,

418 - x = 4

x = 418 - 4

x = 414

Similarly,

Let the number be y,

then,

1866 - y = 3

y = 1866 - 3

y = 1863

So, to get 414 and 1863 they have to be the multiple of a number, here, we looking for the highest value of that number,

Now, we would think let's take the LCM, No LCM gives the common multiple between 414 and 1863, we must find a number whose multiples are 414 and 1863

Thus, we find their HCF,

414 = 2 × 3 × 3 × 23 = 2 × 3² × 23

1863 = 3 × 3 × 3 × 3 × 23 = 3⁴ × 23

Thus, HCF will be the common primes with the lowest power

Thus, HCF = 3² × 23

HCF = 207

Thus,

207 is the largest number which divides 418 and 1866 and leaving behind a reminder of 4 and 3 respectively.

We can check this,

418 ÷ 207

Quotient = 2 and Remainder = 4

1866 ÷ 207

Quotient = 9 and Remainder = 3

Thus, it is true

Hope it helped and you understood it........All the best