Question

Find the largest number that divides 318 and 729 leaving remainders 3 and 4 respectively.

Grade 10, Maths.

(Numbers are 318, and 729)

Answer 1

Answer:

105 is the largest number which divides 318 and 739 leaving remainder 3 and 4 respectively.

Step-by-step explanation:

To find : The largest number which divides 318 and 739 leaving remainder 3 and 4 respectively ?

Solution :

Number which divides 318 and 739 leaving remainder 3 and 4 respectively

318-3=315

739-4=735

Now, We find the Highest common factor of the numbers 315 and 735

315=3\times 3\times 5\times 7315=3×3×5×7

735=3\times 5\times 7\times 7735=3×5×7×7

HCF(315,735)=3\times 5\times 7HCF(315,735)=3×5×7

HCF(315,735)=105HCF(315,735)=105

Therefore, 105 is the largest number which divides 318 and 739 leaving remainder 3 and 4 respectively.

Answer 2

Answer :

The largest number that divides 318 and 729 leaving remainders 3 and 4 respectively is 5.

Explanation :

Let's take a number n.

From the given question, it is clear that, if we subtract 3 and 4 from 318 and 729 respectively, then it divides with n.

∴ (318 - 3 = 315) is a multiple of n

Similarly (729 - 4 = 725) is also a multiple of n.

Now, we can say that n is HCF of (315 and 725)

After that, we have to find the HCF of (315 and 725) either by using Euclid's division lemma or prime factorisation method.

I'm solving it by using prime factorisation method.

★ 315 = 3 × 3 × 5 × 7

★ 725 = 5 × 5 × 29

Here, n = HCF ( 315, 725 ) = 5

Hence, the largest number that divides 318 and 729 leaving remainders 3 and 4 respectively is 5.