1.
There are 16 male students and 20 female students in a Grade 10 math class. The teacher wants to divide the class into groups with the same number of males and the same number of females within each group. What is the greatest number of groups the teacher can make?
Solution: GCF(16,20)=4, therefore the greatest number of groups is 4.
2.
A developer wants to subdivide a rectangular plot of land measuring 600 m by 750 m into congruent square lots. What is the side length of the largest possible square?
Solution: GCF(600,750)=150, so the largest square side length is 150 m.
3.
Factor the trinomial: \(-24c^3d - 40c^2d^2 - 32cd^3\)
Solution: Factor out the GCF \(-8cd\) to obtain \(-8cd(3c^2+5cd+4d^2)\).
4.
What factor must \(-2x^2y^3\) be multiplied by to give a product of \(40x^3y^4\)?
Solution: \((40x^3y^4)\div(-2x^2y^3)= -20xy\).
5.
Determine the least common multiple of 78 and 102.
Solution: 78=2×3×13 and 102=2×3×17. LCM=2×3×13×17=1326.
1 out of 1
