Question

find the largest number that will divide 75 ,123 and 195 leaving the remainder 3 in each case please tell which method is used HCF or LCM

Answer 1

75-3 =72
123-3 = 120
195- 3 = 192
HCF of 72 ,120 192 = 24
HCF is the correct method
the largest nuber that will divide 75,123,195 leaving remainder 3 is 24

Answer 2

The largest number that will divide 75 ,123 and 195 leaving the remainder 3 is 24.

Step-by-step explanation:

Given:

75 ,123 and 195  will be divided by largest number and leaving the remainder 3.

To Find:

The largest number that will divide 75 ,123 and 195 leaving the remainder 3.

Solution:

As given-75 ,123 and 195  will be divided by largest number and leaving the remainder 3.

To make 75, 123 and 195 completely divisible by the greatest number, it is required  to subtract 3 from each term.

$75-3 = 72\\123-3 = 120\\195-3 = 192$

Prime Factors of 72,120 and 192 are following.

$72 = 2\times2\times2 \times3 \times3=2^{3}\times3^{2} \\120 =2\times2\times2 \times3 \times3\times5 = 2^{3}\times3\times5 \\192 = 2\times2\times2 \2\times2\times2\times2 \times3 = 2^{6} \times3$

Hence,HCF  $=2^{3}\times3= 24$

Thus,the largest number that will divide 75 ,123 and 195 leaving the remainder 3 is 24.

PROJECT CODE#SPJ3