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Question
Uma just bought 1 package of 21 binders. She also bought 1 package of 30 pencils. She wants to use all the binders and pencils to create identical sets of class supplies for her friends.
What is the greatest number of items Uma can have in a set?
Uma just bought 1 package of 21 binders. She also bought 1 package of 30 pencils. She wants to use all the binders and pencils to create identical sets of class supplies for her friends.
What is the greatest number of items Uma can have in a set?
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Solution
The correct option is C 3
Uma wants to make identical sets of class supplies.
Since the sets are identical, the number of items in each set will have to be a number that is a common factor of 21 and 30.
Since she is also looking to add the maximum possible number of items in a set, this number will be the greatest number dividing 21 and 30 = HCF (21, 30)
Factors of 21 = 1, 3, 7, 21
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Common factors = 1, 3
⇒ HCF (21, 30) = 3
Uma wants to make identical sets of class supplies.
Since the sets are identical, the number of items in each set will have to be a number that is a common factor of 21 and 30.
Since she is also looking to add the maximum possible number of items in a set, this number will be the greatest number dividing 21 and 30 = HCF (21, 30)
Factors of 21 = 1, 3, 7, 21
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Common factors = 1, 3
⇒ HCF (21, 30) = 3
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