What is 69 divisible by?
Understand the Problem
The question is asking for the numbers that can divide 69 evenly, that is, without leaving a remainder. To solve this, we will identify the factors of 69.
Answer
The factors of 69 are \( 1, 3, 23, \) and \( 69 \).
Answer for screen readers
The factors of 69 are ( 1, 3, 23, ) and ( 69 ).
Steps to Solve
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Identify the Definition of a Factor
A factor of a number is an integer that can be multiplied by another integer to yield that number. For example, if ( a ) is a factor of ( b ), then ( b \div a ) should give an integer result without any remainder. -
List Possible Divisors
To find the factors of 69, we need to consider all positive integers starting from 1 up to ( 69 ). Specifically, we can test integers up to the square root of ( 69 ), which is approximately ( 8.3 ). Thus, we will test integers ( 1 ) through ( 8 ). -
Check Each Integer
For each integer ( n ) from ( 1 ) to ( 8 ), check whether ( 69 \div n ) results in an integer.
- ( 69 \div 1 = 69) (Factor)
- ( 69 \div 2 = 34.5) (Not a factor)
- ( 69 \div 3 = 23) (Factor)
- ( 69 \div 4 = 17.25) (Not a factor)
- ( 69 \div 5 = 13.8) (Not a factor)
- ( 69 \div 6 = 11.5) (Not a factor)
- ( 69 \div 7 = 9.857) (Not a factor)
- ( 69 \div 8 = 8.625) (Not a factor)
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List All Factors Found
The factors found through this process are ( 1 ) and ( 3 ). Since ( 69 ) itself must be included as a factor, we also list ( 69 ) as a factor. -
Final Factor List
The complete list of factors of ( 69 ) includes ( 1, 3, 23, ) and ( 69 ).
The factors of 69 are ( 1, 3, 23, ) and ( 69 ).
More Information
Factors are important in various fields of mathematics, particularly in number theory. Understanding factors helps in simplifying fractions, finding least common multiples, and more. In practical applications, recognizing factors can assist in problem-solving in areas like computer science and engineering.
Tips
- Forgetting to check all integers up to the square root of the number.
- Misinterpreting divisibility; remember that a number is a factor if the division yields a whole number without a remainder.
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