Question

find the gretest number that will divide 138,183,423 leaving reminder each case​

Answer 1

Answer:

In order to make 137, 182 and 422 completely divisible by the greatest number, we need to subtract 2 from each term, so

137-2 = 135, 182-2 = 180 and 422-2 = 420

Now HCF of 135, 180 and 420 is

135 = 3×3×3×5

180 = 2×2×3×3×5

420 = 2×2×3×5×7

Hence HCF of 135, 180 and 420 is 3×5 = 15

Hence the greatest number that will divide 137, 182 and 422 leaving the remainder 2 in each case is 15.

So the correct answer is 15.

Step-by-step explanation:

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Answer 2

Answer: Complete step by step answer:

Now the given three numbers are 138, 183 and 243.

Let us say x is the greatest number that will divide 138, 183 and 243 leaving the remainder 3.

Now we know that if x divides 138, 183 and 243 leaving the remainder 3 then, x will divide 138 – 3, 183 – 3 and 243 – 3.

Hence x divides 135, 180 and 240.

Hence we have x is the greatest number which divides 135, 180 and 240.

Now let us first find the factors of each of the following numbers.

135 = 3 * 3 * 3 * 5 * 5

180 = 2 * 2 * 3 * 3 * 5

240 = 2 * 2 * 2 * 2 * 3 * 5

Hence we can see that the maximum common factor that we get here is 5 * 3 = 15.

Hence the greatest number which divides 135, 180 and 240 is 15.

Hence we get the greatest number which divides 138, 183 and 243 and leaves remainder 3 is 15.

Note: Note that when we say x divides 138 and leaves remainder 3 this means we can write 138 as x.q + 3. Which is nothing but the form dividend = divisor * quotient + remainder. Now since we have 138 = x.q + 3 this means 138 – 3 = x.q. or 135 is divisible by x. This is the concept we have used to find the required number.

Step-by-step explanation: