Division theorem, Euclidean algorithm and Bezout's identity

Division theorem, Euclidean algorithm and Bezout's identity Quiz

Spec 5.1–2 · Edexcel A-Level Further Maths: Quiz

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1. Write $100=7q+r$ with $0\leq r<7$ . What is $r$ ?
- A. $1$
- B. $2$
- C. $3$
- D. $14$
2. Use the Euclidean algorithm to find $\text{hcf}(84,36)$ .
- A. $6$
- B. $9$
- C. $4$
- D. $12$
3. Which equation is Bezout's identity for $14$ and $5$ ?
- A. $14(-1)+5(3)=1$
- B. $14(1)+5(3)=1$
- C. $14(2)+5(-5)=1$
- D. $14(3)+5(-8)=1$
4. Which equation has integer solutions $x,y$ ?
- A. $6x+9y=4$
- B. $10x+15y=8$
- C. $14x+21y=9$
- D. $12x+18y=30$
5. What is the lowest common multiple of $12$ and $18$ ?
- A. $6$
- B. $72$
- C. $36$
- D. $216$