Factors of 175

The factors of 175 are the list of numbers that divide 175 completely without leaving a remainder value. The factors of 175 can be represented in both positive and negative form. Similarly, the pair factors of 175 are also expressed in positive and negative form. For example, the pair factor of 175 is expressed as (1, 175) or (-1, -175). The multiplication of two negative numbers, such as multiplying -1 and -175, will result in the original number 175. Here, we will learn what are the factors of 175, pair factors of 175, how to find the prime factors of 175 using the prime factorization method in a more detailed way.

Table of Contents:

• What are the Factors of 175?
• Pair Factors of 175
• Factors of 175 by Division Method
• Prime Factorization of 175
• Solved Examples
• FAQs

What are the Factors of 175?

The numbers that divide 175 evenly and leave a remainder 0 are the factors of 175. In other words, the numbers that are multiplied together in pairs resulting in the number 175 are the factors of 175. As the number 175 is a composite number, it has many factors other than 1 and 175. Therefore, the factors of 175 are 1, 5, 7, 25, 35 and 175. Likewise, the negative factors of 175 are -1, -5, -7, -25, -35 and -175.

Pair Factors of 175

A pair of numbers that are multiplied together and results in the number 175 is called the pair factor of 175. As discussed above, the pair factors of 175 are expressed in both positive and negative form. Since the number 175 is a composite number, it has more than one factor pair. Thus, the positive and negative pair factors of 175 are given below:

Positive Pair Factor of 175:

Therefore, the positive pair factors of 175 are (1, 175), (5, 35) and (7, 25).

Negative Pair Factor of 175:

Therefore, the negative pair factors of 175 are (-1, -175), (-5, -35) and (-7, -25).

Factors of 175 by Division Method

In the division method, the factors of 175 are found by dividing the number 175 by different integer numbers. If the integer divides 175 exactly without leaving a remainder, then the integer is a factor of 175. Now, let us start dividing 175 by 1 and proceed with the different integers.

• 175/1 = 175 (Factor is 1 and Remainder is 0)
• 175/5 = 35 (Factor is 5 and Remainder is 0)
• 175/7 = 25 (Factor is 7 and Remainder is 0)
• 175/25 = 7 (Factor is 25 and Remainder is 0)
• 175/35 = 5 (Factor is 35 and Remainder is 0)
• 175/175 = 1 (Factor is 175 and Remainder is 0)

If we divide 175 by any numbers other than 1, 5, 7, 25, 35 and 175, it leaves a remainder of some value. Hence, the factors of 175 are 1, 5, 7, 25, 35 and 175.

Prime Factorization of 175

In the prime factorization method, the number 175 is written as the product of its prime factors. Go through the following procedure to find the prime factors of 175 using the prime factorization method.

Take a pair factor of 175, say (1, 175)

As the number 1 is neither prime nor composite, it cannot be split further. Now, take the other factor 175, which is a composite number and it can be factored further into its prime factors.

Thus, 175 is written as the product of 7 and 25. Here, 7 is a prime number and 25 is a composite number, and again the number 25 can be written as the product of 5 and 5.

Now, write the number 175 as the product of its prime factors.

So, 175 is written in the form of 5 x 5 × 7.

Therefore, the prime factorization of 175 is 5 x 5 × 7 or 5² × 7, where 5 and 7 are prime numbers.

Video Lesson on Prime Factors

Examples

Example 1:

Find the common factors of 175 and 174.

Solution:

The factors of 175 are 1, 5, 7, 25, 35 and 175.

The factors of 174 are 1, 2, 3, 6, 29, 58, 87 and 174.

Thus, the common factor of 175 and 174 is 1.

Example 2:

What are the common factors of 175 and 176?

Solution:

Factors of 175 = 1, 5, 7, 25, 35 and 175.

Factors of 176 = 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176.

Therefore, the common factor of 175 and 176 is 1.

Example 3:

Find the common factors of 175 and 179.

Solution:

The factors of 175 are 1, 5, 7, 25, 35 and 175.

The factors of 179 are 1 and 179.

As the number 179 is a prime number, the common factor of 175 and 179 is 1.

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