To find the common factors of 15 and 90, we will follow these steps:
### Step 1: Find the factors of 15
Factors of a number are the integers that can be multiplied together to get that number.
- Start with 1: \( 1 \times 15 = 15 \)
- Next, check 2: 15 is odd, so it is not divisible by 2.
- Check 3: \( 3 \times 5 = 15 \)
- Check 4: 15 is not divisible by 4.
- Check 5: \( 5 \times 3 = 15 \)
- Check 6: 15 is not divisible by 6.
- Check 7: 15 is not divisible by 7.
- Check 8: 15 is not divisible by 8.
- Check 9: 15 is not divisible by 9.
- Finally, check 15: \( 15 \times 1 = 15 \)
**Factors of 15 are:** 1, 3, 5, 15.
### Step 2: Find the factors of 90
Now, we will find the factors of 90.
- Start with 1: \( 1 \times 90 = 90 \)
- Check 2: \( 2 \times 45 = 90 \) (90 is even)
- Check 3: \( 3 \times 30 = 90 \) (9 + 0 = 9, which is divisible by 3)
- Check 4: 90 is not divisible by 4.
- Check 5: \( 5 \times 18 = 90 \) (last digit is 0)
- Check 6: \( 6 \times 15 = 90 \)
- Check 7: 90 is not divisible by 7.
- Check 8: 90 is not divisible by 8.
- Check 9: \( 9 \times 10 = 90 \)
- Finally, check 90: \( 90 \times 1 = 90 \)
**Factors of 90 are:** 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
### Step 3: Identify the common factors
Now, we will compare the factors of 15 and 90 to find the common ones.
- Factors of 15: 1, 3, 5, 15
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
**Common factors are:** 1, 3, 5, and 15.
### Conclusion
The common factors of 15 and 90 are **1, 3, 5, and 15**.
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