What are the Factors of 175?
A factor of a number is an integer that divides the number exactly, that is, leaving no remainder. Here, we will learn about the factors of 175 and solve some fun problems related to the same.
The factors of 175 are those integers that divide 175 without resulting in a remainder. In other words, we can say that the factors of 175 will divide it exactly. The factors of 175 are also the divisors of 175. The factors of 175 cannot be decimals or fractions. The quotient obtained on dividing 175 by its factor is also a factor of 175.
Factors of 175
For example, 5 is a factor of 175 because on dividing 175 by 5, it leaves zero as the remainder and 35 as the quotient. The quotient is also a factor of 175.
Factor List for 175
Prime Factorization of 175
A factor tree can be used to determine the prime factorization of 175, as shown in the figure below:
From the factor tree, we can see that the prime factorization of 175 is: 5 x 5 x 7 = 5\(^2\) x 7.
This means that 5 and 7 are the prime factors of 175.
Factor Pairs of 175
The factor pair of any number is a set of two integers that, when multiplied, result in that number. So, this implies that the two integers are factors of the number.
The factor pair of 175 is the set of two factors of 175 that, when multiplied, give 175 as the product.
Thus, the factor pairs of 175 can be written as:
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Rapid Recall
Solved Factors of 175 Examples
Example 1: There are 3 classes going on a field trip. The teachers plan on using only 2 buses. Can the teachers have an equal number of students on each bus, leaving no student behind?
Solution:
Step 1: Add to find out the total number of students going on the field trip.
50 + 60 + 65 = 175
Step 2: Is the total number of students divisible by the number of buses, which is 2?
Since 175 is an odd number, it is not divisible by 2.
\(\frac{175}{2}\) = 87 R1
Hence, 87 students can fit into both the buses. However, 1 student would be left behind.
So, the teachers will not have an equal number of students on each bus, without leaving a student behind.
Example 2: Find the common factors of 135 and 175.
Solution:
The factors of 135: 1, 3, 5, 9, 15, 27, 45 and 135
The factors of 175: 1, 5, 7, 25, 35 and 175
So, the common factors of 175 and 135 are 1 and 5.
Hence, 135 and 175 have 2 common factors.
Example 3: What are the common factors of 175 and 168?
Solution:
The factors of 175 are 1, 5, 7, 25, 35 and 175
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168.
So, the common factor of 175 and 168 is 1 and 7.
Yes, 5 is a factor of 175. As the number 5 divides 175 exactly, it leaves the remainder 0. So, 5 is a factor of 175.
Yes, 175 is a composite number as it has factors other than 1 and itself, 175. In other words, 175 has more than two factors, which include 5, 7, 25 and 35.
The factors of 175 are 1, 5, 7, 25, 35 and 175
So, the smallest factor of 175 is 1, and the greatest factor is 175 itself.
The factors of 175 are 1, 5, 7, 25, 35, 175
Hence, the sum of all the factors of 175 is
= 1 + 5 + 7 + 25 + 35 + 175 = 248
Hence, the sum is 248.
The factors of 175: 1, 5, 7, 25, 35 and 175. So, the number 175 has 6 factors.