To find all the factors of 420, we will follow these steps:
### Step 1: Start with the number 1
The first factor of any number is always 1. So, we write:
- 1 × 420 = 420
### Step 2: Check for divisibility by 2
Next, we check if 420 is divisible by 2 (the smallest prime number):
- 420 ÷ 2 = 210
So, we have:
- 2 × 210 = 420
### Step 3: Check for divisibility by 3
Now, we check if 420 is divisible by 3:
- 420 ÷ 3 = 140
So, we have:
- 3 × 140 = 420
### Step 4: Check for divisibility by 4
Next, we check if 420 is divisible by 4:
- 420 ÷ 4 = 105
So, we have:
- 4 × 105 = 420
### Step 5: Check for divisibility by 5
Now, we check if 420 is divisible by 5:
- 420 ÷ 5 = 84
So, we have:
- 5 × 84 = 420
### Step 6: Check for divisibility by 6
Next, we check if 420 is divisible by 6:
- 420 ÷ 6 = 70
So, we have:
- 6 × 70 = 420
### Step 7: Check for divisibility by 7
Now, we check if 420 is divisible by 7:
- 420 ÷ 7 = 60
So, we have:
- 7 × 60 = 420
### Step 8: Check for divisibility by 10
Next, we check if 420 is divisible by 10:
- 420 ÷ 10 = 42
So, we have:
- 10 × 42 = 420
### Step 9: Check for divisibility by 12
Now, we check if 420 is divisible by 12:
- 420 ÷ 12 = 35
So, we have:
- 12 × 35 = 420
### Step 10: Check for divisibility by 14
Next, we check if 420 is divisible by 14:
- 420 ÷ 14 = 30
So, we have:
- 14 × 30 = 420
### Step 11: Check for divisibility by 15
Now, we check if 420 is divisible by 15:
- 420 ÷ 15 = 28
So, we have:
- 15 × 28 = 420
### Step 12: Check for divisibility by 20
Next, we check if 420 is divisible by 20:
- 420 ÷ 20 = 21
So, we have:
- 20 × 21 = 420
### Step 13: List all the factors
Now that we have found all the pairs of factors, we can list them:
- The factors of 420 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420.
### Final Answer:
The complete list of factors of 420 is:
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.
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