Question

What is the largest number that divides 437, 732, and 1263 leaving remainder of 24 in each case?​

Answer 1

59 i the answer i hope it helps

Answer 2

Concept-

Use the concept of Euclid's division lemma to find the HCF.

Given-

These three numbers are 437, 732 and 1263.

Find-

Find the greatest number that divides 437, 732, and 1263.

Solution-

Let 'x' be the largest number that leaves the remainder of 24 when dividing these 3 numbers.

Step 1 – Decoding the information entered:

The remainder of 437x is 24.

∴ 437–24 = 413 is divisible by x.

The remainder of 732x is 24.

∴ 732–24 = 708 is divisible by x.

The remainder of 1263x is 24

∴ 1263–24 = 1239 is divisible by x.

So, x divides 413, 708, and 1239 without the remainder.

So x is the common factor of 413, 708, and 1239.

Since x is a largest such number, x is the HCF of 413, 708, and 1239.

Step 2 - Use the Euclidean Distribution Lemma to find the HCF:

Step 1: Apply Euclid's Lemma to 1239 with 708 as the divisor.

1239 = 708 × 1 + 531

The remainder is not zero.

Step 2: Apply Euclid's Lemma to 708 with 531 as the divisor.

708 = 531 × 1 + 177

The remainder is not zero.

Step 3: Apply Euclid's Lemma to 531 with 177 as the divisor.

531 = 177 × 3 + 0

The remainder is 0.

So the divisor of this step of 177 is the HCF of 1239 and 708.

Step 4: Apply Euclid's Lemma to 413 with 177 as the divisor.

413 = 177 × 2 + 59

The remainder is not zero.

Step 5: Apply Euclid's Division Lemma to 177 with 59 as the divisor.

177 = 59 × 3 + 0

The remainder is 0.

∴ The divisor of this step, i.e. 59 is the HCF of 413 and 177.

59 is HCF 413, 708 and 1239

∴ 59 is the largest number that leaves 24 after dividing each of 437, 732 and 1263.

#SPJ2