Factors and multiples: Euclid's algorithm

Advanced Math 7 · Unit 1 · euclid-gcd

euclid-gcd

Name ______________________________Date ______________

1.
Write $360$ in index notation as $2^a \cdot 3^b \cdot 5^c$ . What is $a + b + c$ ?
Answer: ______________
2.
Use Euclid's algorithm to find $\gcd(252, 198)$ , then use $\operatorname{lcm}(a,b) = \dfrac{ab}{\gcd(a,b)}$ . Enter $\operatorname{lcm}(252, 198)$ .
Answer: ______________
3.
A rectangular patio measures $360$ cm by $252$ cm. It is to be covered exactly with identical square tiles, as large as possible, with no cutting. How many tiles are needed?
Answer: ______________
4.
Running Euclid's algorithm on $1071$ and $462$ gives these lines:

$1071 = 2 \times 462 + 147,\qquad 462 = 3 \times 147 + 21,\qquad 147 = 7 \times 21 + 0.$

What is $\gcd(1071, 462)$ ?
1. (A)
  $3$
2. (B)
  $7$
3. (C)
  $21$
4. (D)
  $147$
5.
Two positive integers have a product of $1080$ and a greatest common factor of $6$ . What is their least common multiple?
1. (A)
  $6$
2. (B)
  $36$
3. (C)
  $180$
4. (D)
  $216$
5. (E)
  $1080$