To find the number for which 1, 2, 4, and 8 are factors, we can look for the least common multiple (LCM) of these factors.
1 is a factor of every integer, so it doesn’t affect our calculation. The remaining numbers are 2, 4, and 8. The LCM of these numbers is the smallest number that is a multiple of all three.
Since 8 is the largest of the three numbers, we can check if it’s indeed the LCM. The multiples of 2 are 2, 4, 6, 8, 10, 12, … and so on. The multiples of 4 are 4, 8, 12, … The multiples of 8 are 8, 16, … The smallest number that all these lists have in common is 8.
Hence, the number of which 1, 2, 4, and 8 are factors is 8.