\begin{array}{l}
\text {Q1. Determine the H.C.F. of the following numbers by using Euclid’s algiorithm:} \\
\text {(i) 300,450 } \\
\text {(ii) 399,437} \\
\text {(iii) 1045,1520 } \\ \\
\text {Sol. (i) Taking 450 as dividend and 300 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 150.} \\
\text {Hence, HCF of 300,450 is 150.} \\ \\
\text {(ii) Taking 437 as dividend and 399 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 19.} \\
\text {Hence, HCF of 399,437 is 19.} \\ \\
\text {(iii) Taking 1520 as dividend and 1045 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 95.} \\
\text {Hence, HCF of 1045,1520 is 95.} \\ \\
\text {Q2. Show that the following pairs are co-prime:} \\
(i) \quad 59,97 \\
(ii) \quad 875,1859 \\
(iii) \quad 288,1375 \\ \\
\text {Sol. (i) Taking 97 as dividend and 59 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 1.} \\
\text {Therefore, the numbers 59,97 are co-prime.} \\ \\
\text {(ii) Taking 1859 as dividend and 875 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 1.} \\
\text {Therefore, the numbers 875,1859 are co-prime.} \\ \\
\text {(iii) Taking 1375 as dividend and 288 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 1.} \\
\text {Therefore, the numbers 288,1375 are co-prime.} \\ \\
\text {Q3. What is the H.C.F. of two consecutive numbers? } \\ \\\text {Sol. HCF of two consecutive numbers is 1.} \\
\text {Lets consider 5 and 6 as two consecutive numbers.} \\
\text {Taking 6 as dividend and 5 as divisor.} \\
\end{array}
\begin{array}{l}
\text {Clearly, last divisor is 1.} \\
\text {Therefore, HCF of 5 and 6 is 1.} \\ \\\text {Q4. Write true (T) or false (F) for each of the following statements: } \\
\text {(i) The H.C.F. of two distinct prime numbers is 1.} \\
\text {(ii) The H.C.F. of two co-prime number is 1.} \\
\text {(iii) The H.C.F. of an even and an odd numbers is 1.} \\
\text {(iv) The H.C.F. of two consecutive even numbers is 2.} \\
\text {(v) The H.C.F. of two consecutive odd numbers is 2.} \\ \\\text {Sol. (i) True.} \\
\text {(ii) True.} \\
\text {(iii) False. The HCF of even number 6 and odd number 9 is 3.} \\
\text {(iv) True.} \\
\text {(v) False. The HCF of numbers 25 and 27 is 1.} \\
\end{array}
