Is the first number a factor of the second number? (9) 147
Is the first number a factor of the second number? (9) 147
The Correct Answer and Explanation is:
Answer: No, 9 is not a factor of 147.
Explanation
To determine whether one number is a factor of another, we need to check if the second number can be divided evenly (with no remainder) by the first number.
In this case, we are checking if 9 is a factor of 147. This means we need to check if:147÷9147 \div 9147÷9
Step 1: Perform the Division
147÷9=16.333…147 \div 9 = 16.333…147÷9=16.333…
The result is not a whole number; it’s approximately 16.33 (or exactly 1479=1613\frac{147}{9} = 16 \frac{1}{3}9147=1631).
Since the division does not result in a whole number, 9 is not a factor of 147.
Step 2: Use Multiplication to Double-Check
Let’s check the multiples of 9 close to 147:
- 9×16=1449 \times 16 = 1449×16=144
- 9×17=1539 \times 17 = 1539×17=153
147 is between 144 and 153, meaning it is not a multiple of 9. Therefore, 9 does not divide evenly into 147.
Step 3: Use the Divisibility Rule for 9
A quick test is the divisibility rule for 9: If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
For 147:
- Sum of digits = 1 + 4 + 7 = 12
12 is not divisible by 9, so 147 is not divisible by 9.
Final Conclusion:
Because 147 divided by 9 does not result in a whole number, and it fails the divisibility test for 9, we can conclude that 9 is not a factor of 147.
