Factors of 35

Factors of 35 are 1, 5, 7, and 35. A factor of a number is an integer that divides the given number without leaving a remainder. In other words, Factors of a number are integers that, when multiplied by another whole number, result in the original number without leaving any remainder. In this case, 1, 5, 7, and 35 are factors of 35 because these divide 35 with no remainder.

In this article, we will learn about Factors, Factors of 35, Prime Factors, Prime Factorization of 35, methods to find Factors of a given number such as the Prime Factorization method, and Factor Tree of 35 in detail.

What are Factors of 35?

Factors of 35 are 1, 5, 7, and 35. Factors of a number are integers that, when multiplied by another whole number, results the original number without leaving any remainder. In this case, the number 35 has four factors i.e. 1, 5, 7, and 35 that can completely divide it with no remainder left.

Factors of 35 Calculator

Try out the following calculator to calculate factors of 35

All Factors of 35

The factors of 35 are the integers that divides 35 without leaving a remainder.

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

Explanation:

• 1 as a Factor: Every number is divisible by 1, and 1 multiplied by any number equals the original number.
• 5 as a Factor: 35 divided by 5 equals 7, a whole number without a remainder.
• 7 as a Factor: Similarly, 35 divided by 7 equals 5, another whole number.
• 35 as a Factor: 35 divided by itself equals 1.

Prime Factorization of 35

Prime factorization is the method of expressing a number as a product of its prime factors. To Find Prime Factor of any number we divide it by prime number starting with smallest prime number which is 2 and countinue dividing until further division is not possible, as follows:

• Step 1: Check for smallest prime number that divides 35 completely, i.e 5
• Step 2: Divide 35 by 5 equals 7.
• Step 3: Divide 7 by 7 equals 1. (7 is the smallest prime number that divides 7 completely).

Further division is not possible so, 5 and 7 are the results.

To find Prime Factor of a given number we use a method called Prime Factorization.

Prime Factors of 35

A Prime Factor of a number is a Prime Number that divides the original number exactly, without leaving a remainder. In this case, the Prime Factor of 35 are 5 and 7.

Prime Factors of 35 are 5 and 7.

How to Find Factors of 35?

There are two main methods to Find Factors of 35, they are:

• Multiplication Method
• Division Method

Factors of 35 using Multiplication Method

To find the Factor of 35 using Multiplication Method, we use pairs of numbers whose product is equal to 35. Starting with number 1, explore the pairs of number.

We will obtain,

• 1 × 35 = 35
• 5 × 7 = 35

Therefore, the factor of 35 obtained using Multiplication Method are 1, 5, 7, and 35.

Factors of 35 Using Division Method

To find the Factor using Division Method, we divide 35 by every whole number starting from 1 until we reach 35. The number that divides 35 completely, without leaving a remainder.

Starting with 1.

• 35 / 1 = 35
• 35 / 2 = 17 with remainder 1
• 35 / 3 = 11 with remainder 2
• 35 / 4 = 8 with remainder 3
• 35 / 5 = 7
• 35 / 6 = 5 with remainder 5
• 35 / 7 = 5

We will countinue this process until we reach 35.

• 35 /35 = 1

Therefore, the Factor of 35 using Division Metod are 1, 5, 7, and 35.

Factor Tree of 35

A Factor Tree is a tree like representation of the prime factorization of a number. Here’s the Factor Tree of 35.

Factor Pairs of 35

Factor pairs are pairs of numbers that, when multiplied together, results the original number. In the case of 35, let’s explore both positive and negative factor pairs in detail.

Positive Factor Pairs of 35

Positive factor pairs of 35 are:

• 1 and 35: Multiplied together gives 35.
• 5 and 7: Multiplied together gives 35.

Negative Factor Pairs of 35

Negative factor pairs of 35 are:

• (-1) and (-35): Multiplied together gives 35.
• (-5) and (-7): Multiplied together gives 35.

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Solved Examples of Factors of 35

Example 1: Find the product of all the factors of 35.

Solution:

Product of all the factors of 35: 1 x 5 x 7 x 35 = 1,225

Example 3: Find the largest factor of 35 other than itself.

Solution:

Largest factor of 35 other than itself is 7.

Example 4: Find two pair of factors of 35 whose products is equal to 35.

Solution:

Pairs of factors of 35 whose product is equal to 35 are: (1, 35) and (5, 7).

Example 5: Find all the Prime Factor of 35.

Solution:

Prime Factors of 35 are: 5 and 7.

Practice Problems on Factors of 35

Problem 1: What is the sum of all the factors of 35?

Problem 2: If x is a factor of 35 and x > 1, what is the smallest possible value of x?

Problem 3: Find two factors of 35 whose product is equal to 5.

Problem 4: If x is a factor of both 35 and 5, what are the possible values of x?

Factors of 35 Frequently Asked Questions

What are Factors of 35?

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

How many Factors does 35 have?

There are four factors of the number 35 which are 1, 5, 7, and 35.

What is Largest Factor of 35?

The largest factor of 35 is 35.

Can 35 be Expressed as a Product of its Prime Factors?

Yes, 35 can be expressed as 5 × 7.