1. What is the largest integer that is a factor of all three of the following numbers: 2160, 1344, 1440?

Question

a) 6 b) 8 c) 12 d)16 e) none of these

2. The annual income of a family is budgeted as follows:

1/10 for clothing, 1/3 for food, and 1/5 for rent.

This leaves $1320 for other expenses and savings. Find the annual income.

a) $2156 b) $3600 c) $23,760
d) $39,600 e) none of these answers

Answer 1

2160 = 2*2*2*2*3*3*3*5
1344 = 2*2*2*2*2*2*3*7
1440 = 2*2*2*2*2*3*3*5

HCF = 2*2*2*2*3
= 24

2.
let their income be x
x/10 + x/3 + x/5 + 1320 = x
times 150 , the LCM
15x + 50x + 30x + 198000 = 150x
198000 = 55x
x = 3600

Answer 2

1344 = 1*1344 = 1*2*672 = 1*2*3*224 =
1*2*3*4*56 = 1*2*3*4*7*8.

1440 = 1*1440 = 1*2*720 = 1*2*3*240 =
1*2*3*4*60 = 1*2*3*4*5*12=1*2*3*4*5*6*2

2160 = 1*2160 = 1*2*1080 = 1*2*3*360 =
1*2*3*4*90 = 1*2*3*4*5*18=1*2*3*4*5*6*3

GCF = 4.

2. Income = $X.
(1/10+1/3+1/5)X + 1320 = X
(3/30+10/30*6/30)X + 1320 = x
19x/30 + 1320 = x
Multiply both sides by 30:
19x + 39,600 = 30x
-11x = -39,600
X = $3600