List all divisors of the following integers 28
The correct answer and explanation is:
The divisors of 28 are the integers that divide 28 evenly, meaning without leaving a remainder. To find the divisors of 28, start by finding all of the numbers that can divide it.
Step 1: Find the prime factorization of 28.
28 can be factored as follows: 28=2×2×7=22×728 = 2 \times 2 \times 7 = 2^2 \times 7
This means that 28 is divisible by both 2 and 7.
Step 2: List all divisors.
To find all the divisors of 28, consider all the combinations of powers of its prime factors (2 and 7). The divisors will include:
- 20×70=12^0 \times 7^0 = 1
- 21×70=22^1 \times 7^0 = 2
- 22×70=42^2 \times 7^0 = 4
- 20×71=72^0 \times 7^1 = 7
- 21×71=142^1 \times 7^1 = 14
- 22×71=282^2 \times 7^1 = 28
Thus, the divisors of 28 are:
1, 2, 4, 7, 14, and 28.
Step 3: Verify the divisors.
You can verify these divisors by dividing 28 by each of them:
- 28÷1=2828 \div 1 = 28
- 28÷2=1428 \div 2 = 14
- 28÷4=728 \div 4 = 7
- 28÷7=428 \div 7 = 4
- 28÷14=228 \div 14 = 2
- 28÷28=128 \div 28 = 1
Since each division results in an integer with no remainder, all of these are indeed divisors of 28.
Conclusion:
The divisors of 28 are the numbers 1, 2, 4, 7, 14, and 28. These are all the integers that divide 28 evenly.