Question

The greatest number that will divide 76, 112, 172 and 184 so as to leave remainder 40 in each case is 3K. Find the value of K.

Answer 1

Step-by-step explanation:

plz mark brainleist. . . . follow for every answer

Answer 2

Given:

The greatest number that will divide 76, 112, 172, and 184 to leave the remainder of 40 in each case is 3K

To Find:

The value of K.

Solution:

To find the number which will leave the remainder of 40 in each case

We will first subtract 40 from all the four numbers

76 - 40 = 36

112-40 = 72

172- 40 = 132

184- 40 = 144

Now, we will find the H.C.F (Highest Common Factor) of all the numbers

Let us factorize all the numbers

36 = 2×2×3×3

72= 2×2×2×3×3

132 = 2×2×3×11

144 = 2×2×2×2×3×3  

In all the numbers 2×2×3 is common

So, H.C.F =2×2×3

                  =12

The greatest number that will divide 76, 112, 172, and 184 to leave the remainder of 40 in each case is 12

Now, it is given that the number is 3K

So,

So,

3K = 12

K = 4

Hence, the value of K = 4