Arianna is packing scented candles and candle holders into gift boxes. She has 84 candles and 48 holders, and each box must contain both items. She puts the same number of candles in each box, and the same number of holders in each box. What is the maximum number of gift boxes Arianna can pack, and how many scented candles and candle holders will each box have?
To find the maximum number of gift boxes Arianna can pack, we need to find the greatest common divisor of 84 and 48.
The prime factorization of 84 is 2^2 * 3 * 7.
The prime factorization of 48 is 2^4 * 3.
To find the greatest common divisor, we take the lowest power for each common prime factor.
So, the greatest common divisor of 84 and 48 is 2^2 * 3 = 12.
Therefore, Arianna can pack a maximum of 12 gift boxes.
Each box will have 84/12 = <<84/12=7>>7 scented candles and 48/12 = <<48/12=4>>4 candle holders. Answer: \boxed{7}.