Question

Find the largest number wch divides 224, 250 and 302 and leaves remainder 3 in each case.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

∴ The largest number which divides 224, 250 and 302 and leaves remainder 3 in each case = 13

Step-by-step explanation:

To find,

Largest number which divides 224, 250 and 302 and leaves remainder 3 in each case.

Solution:

Let X be the largest number which divides 224, 250 and 302 and leaves remainder 3 in each case,

Then we have, X is the largest number which divides 224 - 3, 250 -3 and 302 - 3 and leaves reminder zero.

That is X is the largest number which divides 221, 247, 299

Since the largest number divides any two more numbers is the HCF of that numbers we have

X is the HCF of 221, 247, 299

To find HCF(221,247,299)

Prime factorization of 221 = 13 × 17

Prime factorization of 247 = 13 × 19

Prime factorization of 299 = 13 × 23

The common factor 221,247,299 = 13

The highest common factor of 221,247,299 = 13

X = 13

∴ The largest number which divides 224, 250 and 302 and leaves remainder 3 in each case = 13

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