The factors of 105 are defined as the numbers which when divided to 105 should not leave any remainder. This means, 105 must be completely divisible by such a number that it does not leave any remainder.
The integer 105 can be divided only into three numbers – 1, 3, 5, 7. It means, the product of 1, 3, 5, 7 will result in the number 105.
Moreover, the number 105 will have the following factors: 1, 3, 5, 7, 15, 21, 35 and 105. Therefore, the largest factor of 105 is 35, which is a composite number.
The largest prime factor of 105 is 7. The number 105 can be written as: 105 = 3 x 5 x 7. However, 105 will have the following categories of factors-
Positive factors: 1, 3, 5, 7, 15, 21, 35 and 105 Prime factors: 1, 3, 5, 7 Negative factors: -3, -5, -7 Prime factorization of 105 = 3 x 5 x 7
The factors of 105 can be found by two methods –Long-division method and Prime factorization method.
The prime factorization method is the most common method to represent several numbers, including 105.
Prime factorization also has another form, the prime factor tree method, which is a visual method to represent factors of 105.
It helps in determining various prime factors of 105. A factor tree is not unique for a given number. Instead of expressing 105 as 35 x 3, or 21 x 5, we can represent 105 as 3 x 5 x 7.
We need to divide 105, from the smallest number to the largest number so that it completely divides the number-
Prime factorization of 105 using the prime factorization method is 3 x 5 x 7.
Example 1:
What are the common factors of 35 and 105?
Solution:
The factors of 35 are 7 and 5. The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105. Thus, the common factors of 35 and 105 are 7 and 5.