Numbers between 1 and 150 divisible by 4
The correct answer and explanation is:
To find numbers between 1 and 150 that are divisible by 4, we need to determine which numbers satisfy the condition:
A number is divisible by 4 if the result of dividing it by 4 is an integer. This means we need to find multiples of 4 within the range of 1 to 150.
The smallest multiple of 4 within this range is 4 (since 4 ÷ 4 = 1), and the largest multiple of 4 within this range is 148 (since 148 ÷ 4 = 37). So, we are looking for numbers between 4 and 148 that are divisible by 4.
The multiples of 4 in this range are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, and 140.
These numbers are all divisible by 4 because when each is divided by 4, the result is an integer.
To explain how we find these numbers systematically:
- The first multiple of 4 in the range is 4, and the second one is 8 (4 × 2).
- To generate subsequent multiples of 4, continue adding 4 to the previous multiple, i.e., 8 + 4 = 12, 12 + 4 = 16, and so on, until you reach 148.
- The number of multiples can also be found by dividing 150 by 4, which gives 37.5. Since 37 is the greatest whole number, it indicates that 37 multiples of 4 fit within the range from 1 to 150, with the highest multiple being 4 × 37 = 148.
Thus, the numbers divisible by 4 between 1 and 150 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144.