Factors of 35 | Pair Factors & Prime Factorization

Factors Of 35

A factor of 35 is a number that divides 35 exactly without leaving a remainder. For 35, there are four factors, where 35 is the largest factor and 1 is the smallest factor. 1, 5, 7, and 35 are these factors. 

In the case of multiplying two numbers in pairs resulting in the original number, we have the pair factor of 35. There are two pair factors (1, 35) and (5, 7). As a result, these factors can only be positive integers and cannot be decimals or fractions.  The sum of all the factors of 35 is 48.

What are the Factors of 35?

Factors of 35 are the numbers that divide 35 exactly. To divide 35, a number should leave zero as a remainder. It has more than two factors because it is a composite number.

Therefore, the factors of 35 are 1, 5, 7, and 35.

Likewise, 35’s negative factors are -1, -5, -7, and -35.

Pair Factors of 35

To get the number 35, multiply two numbers together, and the result is the pair factor of 35. This number has both positive and negative pair factors. 

As a result of 35, the following pair factors are positive and negative:

Positive Pair Factors of 35:

Negative Pair Factors of 35:

How to Find Factors of 35?

It is possible to find the factors of 35 by using two methods:

• Division method
• Prime factorization method

Factors of 35 by Division Method

Divide 35 by different integers to find the factors of 35 using the division method. An integer that divides 35 completely and leaves 0 as a remainder is a factor of 35. Let’s now divide 35 by 1 and then continue with different integers.

• 35/1 = 35 
• 35/5 = 7 
• 35/7 = 5 
• 35/35 = 1 

When 35 is divided by any number other than 1, 5, 7, and 35, it leaves a remainder of some value. Therefore, the factors of 35 are 1, 5, 7, and 35.

Prime Factorization of 35

Prime factorization of 35 means writing 35 as the product of its prime factors. Using prime factorization, let us determine the prime factors of 35.

• Consider the pair factor of 35, say (1, 35)
• There is no further factoring possible for the number 1. Instead, consider the composite number 35
• Next, divide the composite number by its prime factors.
• In other words, 35 is the product of 5 and 7.
• There are two prime factors, 5 and 7. As a result, 35 = 5 x 7

Consequently, the prime factorization of 35 is 5 × 7 or 5¹ × 7¹.

Facts to be Noted

• Factors of 35= 1, 5, 7 and 35
• Pair Factors of 35= (1, 35) and (5, 7)
• Prime factors of 35= 5 and 7
• Prime factorization of 35= 5¹ x 7¹

Solved Examples 

Example 1:

What are the common factors between 35 and 34?

Solution:

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

1, 2, 3, 4, 6, 8, 12,and 24 are the factors of 24.

Hence, 35 and 24 have a common factor of 1.

Example 2:

Calculate the common factors of 24 and 36.

Solution:

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.

36 has the factors 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Therefore, 24 and 36 have a common factor of 1, 2, 3, 4, 6, and 12.

Example 3:

Find the common factor between 35 and 41.

Solution:

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

1 and 41 are the factors of 41.

Since 41 is a prime number, the common factor between 35 and 41 is only 1.

FAQs

Conclusion

we hope that with the above illustration you are now in a better position to understand the factors of 35.

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