To find the factors of 356, we will identify all the numbers that can divide 356 without leaving a remainder. Here’s a step-by-step solution:
### Step 1: Start with 1
The first factor of any number is always 1.
- **Factor found: 1**
### Step 2: Check for divisibility by 2
Next, we check if 356 is divisible by 2 (the smallest prime number). Since 356 is an even number, it is divisible by 2.
- **Calculation:** 356 ÷ 2 = 178
- **Factor found: 2 and 178**
### Step 3: Check for divisibility by 3
Now, we check if 356 is divisible by 3. To do this, we can sum the digits of 356 (3 + 5 + 6 = 14) and see if 14 is divisible by 3. Since 14 is not divisible by 3, 356 is not divisible by 3.
- **No factor found: 3**
### Step 4: Check for divisibility by 4
Next, we check if 356 is divisible by 4. A number is divisible by 4 if the last two digits form a number that is divisible by 4. The last two digits of 356 are 56.
- **Calculation:** 56 ÷ 4 = 14
- **Factor found: 4 and 89**
### Step 5: Check for divisibility by 5
Since 356 does not end in 0 or 5, it is not divisible by 5.
- **No factor found: 5**
### Step 6: Check for divisibility by 6
Since 356 is not divisible by 3 (as found earlier), it cannot be divisible by 6.
- **No factor found: 6**
### Step 7: Check for divisibility by 7
Now we check if 356 is divisible by 7.
- **Calculation:** 356 ÷ 7 = 50.857 (not a whole number)
- **No factor found: 7**
### Step 8: Check for divisibility by 8
Next, we check if 356 is divisible by 8.
- **Calculation:** 356 ÷ 8 = 44.5 (not a whole number)
- **No factor found: 8**
### Step 9: Check for divisibility by 9
As previously determined, since 356 is not divisible by 3, it is also not divisible by 9.
- **No factor found: 9**
### Step 10: Check for divisibility by 10
Since 356 does not end in 0, it is not divisible by 10.
- **No factor found: 10**
### Step 11: Check for divisibility by 89
After checking up to the square root of 356 (which is approximately 18.87), we find that 89 is a factor.
- **Calculation:** 356 ÷ 89 = 4
- **Factor found: 89**
### Step 12: Check for divisibility by 178
We already found that 178 is a factor when we divided by 2.
- **Factor found: 178**
### Step 13: Include the number itself
Finally, the last factor is the number itself, which is 356.
- **Factor found: 356**
### Summary of Factors
The complete list of factors of 356 is:
1, 2, 4, 89, 178, and 356.
### Final Answer
Hence, the factors of 356 are: **1, 2, 4, 89, 178, 356.**
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