Factors of 69
Numbers that exactly divide 69, that is, leave zero as the remainder on division are known as the factors of 69. In other words, factors of 69 can divide 69 into equal parts.
Let’s consider an example:
3 is a factor of 69 because on dividing 69 by 3 we get zero as the remainder. The quotient, 23 is also a factor of 69.
Therefore, to check whether a number is a factor of 69, divide 69 by that number, if the remainder is zero, then that number is said to be a factor of 69.
Factor list of 69
If we continue checking for numbers greater than 6 we will notice that the factor pairs will start to repeat. Therefore, the factors of 69 are 1, 3, 23 and 69.
Prime factors of 69
The number 69 is a composite number, that is, it has more than two factors. To carry out the prime factorization of 69, we will keep dividing 69 by its prime factors, until we get the result as 1.
So the prime factors of 69 are 3 and 23 and its prime factorization is:
\(69 = 23 \times 3.\)
Factor pairs of 69
The factor pair of 69 is a set of two factors of 69 that when multiplied together give the product as 69. Factor pairs of a number can be listed from the set of factors of the number.
The factor pairs of 69 are: (1, 69) and (3, 23).
Solved Examples
Example 1: Find the factors common between 72 and 69.
Solution:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Factors of 69 = 1, 3, 23 and 69.
Therefore, the factors common between 72 and 69 are 1 and 3.
Example 2: Liza decides to donate 69 stationary items among 20 children in an orphanage. How can she divide the items equally?
Solution:
\(69 \div 20 = 3 R9.\)
As 20 is not a factor of 69, we get a remainder here of 9.
Therefore, to divide the stationary items equally, Liza would have to give the children 3 items each but she would be left with 9 items.
The factors of 69 are 1, 3, 23 and 69. So, the lowest factor of 69 is 1 and the highest factor is 69 is 69 itself.
Numbers that have exactly two factors, 1 and the number itself, are called prime numbers.
The number 69 is odd as it is not exactly divisible by 2.