Factors and Multiples

GCF

100

What is the GCF of 9 and 36?

9

200

Find the GCF of 45, 78, and 96

3

300

A company planned to donate 640 packs of cookies, 320 bottles of mineral water, and $800 worth of cash to a senior center. Suppose the maximum number of packs of cookies, bottles of mineral water, and cash will be placed equally in gift bags before the donation.

(a) How many gift bags are needed?

(b) List the content in each gift bag.

(a) 160 gift bags are needed.

(b) Each bag will have 4 packs of cookies, 2 bottles of mineral water, and $5 cash.

LCM

100

Find the LCM of 5, 18, and 20

180

200

Find the LCM of 5, 6, 8

120

300

Suppose trains on each of three separate lines (NS, EW, and NE) leave together at 2:30 p.m., which falls within the non-peak period from 2 to 5 p.m. Suppose also that the trains on the NS, EW, and NE lines leave regularly at 5 min, 6 min, and 8 min intervals respectively during the non-peak period.

(i) How long, in hours, will it take for the trains on all three lines to leave together again?

(ii) What is that time?

(i) It will take the trains 2 hours to leave together again.

(ii) 4:30 p.m.

P.F.

100

Find the smallest number that has the prime factors of 2, 3, 5, and 7.

210

200

Find the p.f. of 3,375 and write your answer in exponential form. 

BONUS (ALL TEAMS):  What is the smallest 3-digit number that is a factor of 3,375

3³ x 5³

135

300

Find the p.f. of the following numbers and write your answer in exponential notation.

27                 99                   135

(a) Find the GCF in p.f. form

(b) Find the LCM in p.f. form

(a) 3²

(b) 3³ x 5 x 11

Squares

100

sqrt(64)

sqrt(64) = 8

200

sqrt(576)

sqrt(576) = 24

300

What prime factor is needed to make this number a perfect square? Explain why you know.

2² x 5⁴ x 7⁸ x 11³

A prime factor of 11 is needed. For this number to be a perfect square, the prime factors must be divided into two equal groups. 

Cubes

100

Find the cube root of 27

3

200

Find the cube root of 

2^6 * 5^3 *11^3

2^2 * 5 * 11 = 220

300

What prime factor is needed to make this number a perfect cube? How many more? Explain why you know.

2³ x 5⁷ x 7⁹ x 11⁶

Two prime factors of 5 are needed. To be a perfect cube, you have to be able to divide your prime factors into three equal groups. 

2³ x 5⁹ x 7⁹ x 11⁶