To find the factors of 120, we will identify all the pairs of numbers that multiply together to give 120. Here’s how we can do it step by step:
### Step 1: Start with the number 1
The first factor is always 1, since 1 multiplied by any number gives that number itself.
- Pair: \(1 \times 120\)
### Step 2: Move to the next whole number, which is 2
Check if 120 is divisible by 2. Since 120 is even, it is divisible by 2.
- Pair: \(2 \times 60\)
### Step 3: Check for the next whole number, which is 3
Now, check if 120 is divisible by 3. To do this, add the digits of 120 (1 + 2 + 0 = 3), which is divisible by 3.
- Pair: \(3 \times 40\)
### Step 4: Check for the next whole number, which is 4
Check if 120 is divisible by 4. Since 120 ends in 0, it is divisible by 4.
- Pair: \(4 \times 30\)
### Step 5: Check for the next whole number, which is 5
Check if 120 is divisible by 5. Since it ends in 0, it is divisible by 5.
- Pair: \(5 \times 24\)
### Step 6: Check for the next whole number, which is 6
Check if 120 is divisible by 6. Since the sum of the digits (1 + 2 + 0 = 3) is divisible by 3 and it is even, 120 is divisible by 6.
- Pair: \(6 \times 20\)
### Step 7: Check for the next whole number, which is 8
Check if 120 is divisible by 8. Since 120 divided by 8 equals 15, it is divisible.
- Pair: \(8 \times 15\)
### Step 8: Check for the next whole number, which is 10
Check if 120 is divisible by 10. Since it ends in 0, it is divisible by 10.
- Pair: \(10 \times 12\)
### Step 9: List all the factors
Now, we can list all the factors we found:
- 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
### Final Answer:
The factors of 120 are: **1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120**.
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