Answer :
The H.C.F. of the numbers 95, 76, and 114 using the division method is [tex]\( \boxed{19} \).[/tex]
To find the Highest Common Factor (H.C.F.) of the numbers 95, 76, and 114 using the division method, we proceed step by step.
Find the H.C.F. of 95 and 76
Divide 95 by 76
[tex]\[ 95 \div 76 = 1 \quad \text{remainder} \quad 19 \][/tex]
Now, divide 76 by 19
[tex]\[ 76 \div 19 = 4 \quad \text{remainder} \quad 0 \][/tex]
Since the remainder is now 0, the divisor at this step, which is 19, is the H.C.F. of 95 and 76.
Find the H.C.F. of the result from Step 1 (which is 19) and 114
Divide 114 by 19:
\[ 114 \div 19 = 6 \quad \text{remainder} \quad 0 \][tex]\[ 114 \div 19 = 6 \quad \text{remainder} \quad 0 \][/tex]
Again, since the remainder is 0, the divisor at this step, which is 19, is also the H.C.F. of 95, 76, and 114.
