| Step 1: \[\text{1}0\text{32}=\text{4}0\text{8}\times \text{2}+\text{216}\] |
| Step 2: ___________ |
| Step 3: ___________ |
| Step 4: \[\text{192 }=\text{24}\times \text{8}+0\] |
| (i) 408=2161+1921 |
| (ii) 408=216+180+12 |
| (iii) 216 =192 1 + 24 |
| (iv) 192 = 24 8 + 0 |
A) (i) and (ii)
B) (i) and (iii)
C) (ii) and (iii)
D) (iii) and (iv)
Correct Answer: B
Solution :
Using Euclid's algorithm, H.C.F. of 408 and 1032 is: Step 1: \[\text{(25}\times \text{7)cm}\] Step 2: \[~(\text{2}\times \text{52}\times \text{73) cm}\] Step 3: \[=(\text{25}\times \text{7})\text{(2}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{3}}}\text{) c}{{\text{m}}^{\text{2}}}\] Step 4: \[={{\text{2}}^{\text{6}}}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{4}}}\text{c}{{\text{m}}^{\text{2}}}\] Hence, the required steps are (i) and (iii) only.
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