Question

find the greatest number which divides 137 ,167 and 152 leaving a remainder 2 in each case.

Answer 1

hi

aim: to find the greatest number which divides 137 ,167 and 152 leaving a remainder 2 in each case.

=> 137 - 2 = 135

167 - 2 = 165

152 - 2 = 150

so the obtained numbers are 135 :165 and 150

now let us find their hcf

135 =  1,3,5,9,15,27,45,135

165 = 1, 3, 5, 11, 15, 33, 55, 165

150 =  1,2,3,5,6,10,15,25,30,50,75,150

hcf = 15

hence 15 is the  the greatest number which divides 137 ,167 and 152 leaving a remainder 2 in each case.

hope it helps u

:)

Answer 2

Answer:

The required largest number is 15.

Step-by-step explanation:

Given : The greatest number which divides 137 ,167 and 152 leaving a remainder 2 in each case.

To find : The number ?

Solution :  

First we find the difference between numbers. and reminder.

The required numbers are  

137-2=135

167-2=165

152-2=150

Now, We find the HCF of 135,165 and 150.

$135=3\times 3\times 5$

$165=3\times 5\times 11$

$150=2\times 3\times 5\times 5$

$HCF(135,165,150)=3\times5=15$

Therefore, The required largest number is 15.