Lucy has 80 foreign stamps and 128 Philippine stamps. She separates the two kinds of stamps in her album and she puts the biggest and the same number of stamps of each kind on a page. If all pages with stamps in her album are full and there are none left over how many stamps are on each page

To find out how many stamps are on each page, we need to find the greatest common divisor (GCD) of 80 and 128. The GCD represents the largest number that divides both 80 and 128 without leaving a remainder.

To calculate the GCD, we can use the Euclidean algorithm:

1. Divide 128 by 80:
128 ÷ 80 = 1 remainder 48

2. Divide 80 by 48:
80 ÷ 48 = 1 remainder 32

3. Divide 48 by 32:
48 ÷ 32 = 1 remainder 16

4. Divide 32 by 16:
32 ÷ 16 = 2 remainder 0

Since we have reached a remainder of 0, we stop. The last nonzero remainder, which in this case is 16, is the GCD of 80 and 128.

Hence, there will be 16 stamps on each page in Lucy's album.

To find out how many stamps are on each page, we need to determine the least common multiple (LCM) of the quantities of foreign stamps and Philippine stamps that Lucy has. The LCM is the smallest number that is divisible by both numbers without leaving any remainder.

First, let's determine the prime factorization of both quantities:

80 foreign stamps: 2² × 5 × 2
128 Philippine stamps: 2⁷

Now, let's find the LCM by taking the highest power of each prime factor:

LCM = 2⁷ × 5 × 2 = 2⁸ × 5 = 256 × 5 = 1280

Therefore, there will be 1280 stamps on each page.