Ken had 405 stickers. He gave his stickers equally to some friends. He gave the stickers to fewer than 10 friends. He had no stickers left. How many friends could he give his stickers to?
Answer (2)
Ken can give his 405 stickers to 1, 3, 5, or 9 friends, as these numbers are the factors of 405 that are less than 10. Each amount given ensures he has no stickers left over. Each friend will receive an equal number of stickers in these scenarios.
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To solve this problem, we need to determine how many friends Ken could give his stickers to. We know the following:
Ken has 405 stickers.
He divided these stickers equally among his friends.
There were fewer than 10 friends, and no stickers were left.
This means that 405 must be divisible by the number of friends. We need to find the divisors of 405 that are less than 10.
Let's find the divisors:
First, calculate the prime factorization of 405. We can see that:
405 = 5 × 3 4
From this factorization, the divisors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405.
The divisors of 405 that are less than 10 are 1, 3, 5, and 9.
Therefore, Ken could give his stickers to 1, 3, 5, or 9 friends.
