Question

A florist has 48 roses, 32 tulips and 16 carnations which she must use to create bouquets. What is the largest number of bouquets she can make without having any flowers left over?

Answer 1

....we decompose 48,32 and 16 into products of prime factor

48= 2*24

24 =2*12

12=2*6

6=2*3

3=3*1

48 = 2^4*3

32 =2*16

16=2*8

8=2*4

4=2*2

2=2*1

32 = 2^5

16=2*8

8=2*4

4=2*2

2=2*1

16 = 2^4

gcd(48;32;16)=2^4=16

she can make 16 bouquets without having any flowers left

Explanation: