Question

Which is the largest number that divides 185 and 167 and leaves remainder 5?

Answer 1

Hi there!
Here's the answer:

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¶¶¶ Type of problem :

To find the largest No. that will divide x and y leaving remainder 'r' in each case



¶¶¶ Approach to problem:

• Find (x-r) & (y-r)
• Find HCF(x-r , y-r)

---- This value of HCF gives the Highest divisor that will divide x & y leaving remainder 'r' in both the case.


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¶¶ SOLUTION:

Given,
x = 185 & y = 167 & r = 5

x-r = 185 - 5 = 180
y-r = 167 - 5 = 162

Now, find HCF(162, 180)

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^^ Method of division (or) Method of prime factors can be used to find HCF

Here,Going to use Division Method of finding HCF :


¶¶¶ STEPS :

(1)• Divide Greater No. by Smaller No.
(2)• Divisor of (1) is divided by its remainder
(3)• Divisor of (2) is divided by its remainder
This continues until no remainder is left

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162) 180 ( 1
………162
----------------------------
…………18) 162 ( 9
………………162
-----------------------------
..……………[{ 0 }]


•°• HCF (162, 180) = 18

•°• Required Largest divisor that divides 185 & 167 leaving 5 as remainder in each case = 18

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Hope it helps

Answer 2

Answer:

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Step-by-step explanation:

•°• HCF (162, 180) = 18

•°• Required Largest divisor that divides 185 & 167 leaving 5 as remainder in each case = 18