A medium question on divisibility and factors for P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P4 and P5 qualifying rounds and finals; harder ones use how many factors a number has, and square numbers.
The question
A florist has 60 red roses and 108 white roses.
She wants to tie all of them into identical bunches: every bunch has the same number of red roses and the same number of white roses, with none left over.
If she makes as many bunches as possible, how many roses are in each bunch?
Show the hints (2)
💡Hint 1: The number of bunches must share out both the 60 red and the 108 white roses exactly.
💡Hint 2: First find the largest number that divides both 60 and 108: that is the most bunches.
Worked solution
Have a go first, then read the solution step by step.
1.Both colours are cut into the same number of bunches, all alike, so the number of bunches must divide both 60 and 108.
2.Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. The blue ones are common factors.
3.The largest common factor is 12, so at most 12 bunches.
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