Lucia has 48 markers and 64 stickers that she wants to give as favors for a party. She wants to put an equal number of markers and an equal number of stickers into each favor bag. She uses all the markers and stickers.
Use the drop-down menus to complete the statements below about the number of bags Lucia can make.
The greatest number of bags Lucia can make is ____. Each of these bags will have ____ markers and ____ stickers.
If she used more bags, ____.
She could use ____ bags, but this is not the greatest number she could use.
To find the greatest number of bags Lucia can make, we need to determine the greatest common divisor (GCD) of the number of markers (48) and stickers (64).
1. Finding the GCD:
– The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
– The factors of 64 are: 1, 2, 4, 8, 16, 32, 64.
– The common factors are: 1, 2, 4, 8, 16.
– The greatest common factor is 16.
2. Calculating the number of bags and items in each bag:
– The greatest number of bags is 16.
– Each bag will have:
– Markers: 48 (total markers) ÷ 16 (bags) = 3 markers per bag.
– Stickers: 64 (total stickers) ÷ 16 (bags) = 4 stickers per bag.
Now we can fill in the statements:
– The greatest number of bags Lucia can make is 16. Each of these bags will have 3 markers and 4 stickers.
3. If she used more bags, she would not be able to distribute all the markers and stickers equally since 16 is the greatest number that