Factors

# Factors of 35 | Prime Factorization of 35 | Factor Tree of 35

Written by Prerit Jain

Updated on: 18 Aug 2023

Contents

### Factors of 35 | Prime Factorization of 35 | Factor Tree of 35

**Factors of 35: ** A set of numbers that divides the given number evenly is referred to as its factors. In this case, we will take 35 as the given number. The numbers 1, 5, 7, and 35 divide the number 35 completely.

**Hence, the four factors of 35 are 1, 5, 7, and 35.**

The **factors** of a number can be positive or negative. They can also be written in the pairs. This means, multiplying the set of two factors in pairs gives the original product (35). In this article, we will discuss how to find factors of 35, its prime factorization, and factor trees with solved examples. To know more, keep reading.

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## What Are the Factors of 35?

The factors of 35 are those numbers that divide the number (35) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 35 has both positive and negative factors.

Factors of 35: 1, 5, 7 and 35 |

Negative Factors of 35: –1, -5, -7 and -35 |

Prime Factorization of 35: 5 X 7 |

Pair Factors of 35: (1, 35) and (5, 7) |

Prime Factors of 35: 5, 7 |

Sum of Factors of 35: 48 |

Sum of Prime Factors of 35: 12 |

## What Are the Factors of 35 in Pairs?

A pair factor of 35 is a combination of two numbers. These numbers, when multiplied together give the product of 35. These pair factors are also written in positive and negative pairs as shown in the table below:

### Positive Pair Factors of 35

The positive pair factors of 35 are (1, 35) and (5, 7).

### Negative Pair Factors of 35

The negative pair factors of 35 are (-1, -35) and (-5, -7).

## How To Find Factors of 35 Using the Division Method?

We are using the division method, to find the factors of 35. This method needs you to multiply a sequence of natural integers by 35. The numbers that divide the 35 completely without leaving a remainder are the factors of 35. The following are the detailed steps for finding factors of 35 using the division method:

35 ÷ 1 = 35

35 ÷ 5 = 7

35 ÷ 7 = 5

35 ÷ 35 = 1

Therefore, we can see that 1, 5, 7, and 35 are the numbers that do not leave any remainder when divided by 35. Hence, the factors of 35 are 1, 5, 7, and 35.

## What Is the Prime Factorization of 35?

Check if the given number is a prime number. If it is, then it can have only two factors: 1 and 35. If the given number is composite, then it can have more than two factors.

Since 35 is a composite number, it has more than two factors. Hence, we can use the prime factorization method to find the factors of 35.

The steps to find prime factors of 35 using the prime factorization method are given below:

**Step 1:** Divide the number 35 with the smallest prime number that can divide it. The smallest prime number that is divisible by 35 is 5. So, 35 ÷ 5 = 7

**Step 2:** The next step is to divide the quotient of the previous equation. But, 7 also happens to be a prime number. So it can only be divided by 1 and 7. So, 7 ÷ 7 = 1. The quotient is 1. Since 1 cannot be divided further, the prime factors of 35 are 5 X 7. We can also write it down as 5 and 7, as both of them are prime numbers.

Image representation of the prime factorization of 35:

## What Is the Factor Tree of 35?

Students can also use the factor tree to find the prime factors of 35. In this method, we will place the number 35 at the top. 35 will now branch out as a set of any of its factors of 35. These factor pairs will further be split into more factors. This process shall go on until all the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 35.

**Step 1: **Place the number 35 on top of the factor tree. Let’s write down 35 in pairs: 5 and 7.

**Step 2:** Since 5 and 7 are both prime numbers, we can no longer separate them. Now the branches in the factor tree will all be prime numbers.

Hence, circling all the branches, 5 X 7 = 35, which are 35 prime factors.

The factor tree of 35 can be written in many ways. The visual representation is given below:

## Solved Examples on Factors of 35

Here are some solved examples of factors of 35:

**What is the sum of all the factors of 35?**1, 5, 7, and 35 are the 35 factors.

1 + 5 + 7 + 35 = 48

Hence, 48 is the sum of all 35 factors.

**What are the factors and prime factors of 35?**The factors of 35 are 1, 5, 7, and 35.

The prime factors of 35 are 5 X 7.

**What’s the highest common factor between 40 and 35?**The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

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

Hence, the common factors of 40 and 35 are 1 and 5.

The highest common factor between 40 and 35 is 5.

**What’s the highest common factor between 35 and 91?**The factors of 35 are 1, 5, 7, and 35.

Factors of 91 are 1, 7, 13, and 91.

Hence, from the above, the common factors of 35 and 91 are 1 and 7.

The highest common factor between 35 and 91 is 7.

**Is 7 a factor of 35?**Yes, 7 is a factor of 35.

35 ÷ 5 = 7

**What are the factors of -35?**The factors of -35 are -1, -5, -7 and -35.

**What are the common factors of 35 and 77?**To find the common factors of 35 and 77, we need to find the factors of both numbers.

Factors of 35: 1, 5, 7 and 35

Factors of 77: 1, 7, 11 and 77

Hence the common factors of 35 and 77 are 1 and 7.

**What are all the factors of 35?**The factors of 35 are 1, 5, 7, and 35.

**What are the factors of 35 that are composite?**Any number which has more than 2 factors is known as a composite number. The number which has more than 2 factors in factors of 35 is 35.

**What factors of 35 are multiples of 5?**The factors of 35 that are multiples of 5 are 5 and 35.

5 x 1 = 5

5 x 7 = 35.

**How many factors of 35 are odd?**All factors of 35 are odd numbers and they are 1, 5, 7, and 35.

**What are** the factors of 42 and 35?

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

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

**What are the common factors of 100 and 35?**To list out the common factors of 100 and 35, we need to find the factors of both numbers.

Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100

Factors of 35: 1, 5, 7 and 35

From the above, the common factors of 100 and 35 are 1 and 5.

**How many different factors are there for the number 35?**A total of 4 factors are there for the number 35 and they are 1, 5, 7, and 35.

**What factors of 35 are multiples of 7?**The factors of 35 that are multiples of 7 are 7 and 35.

**How many pair factors are there in 35?**A total of 2 pairs are there in factors of 35.

**What is the largest factor of 35?**The largest factor of 35 is 35.

The second largest factor of 35 is 7.

**Looking to Learn Math? Explore Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.**

## FAQ’s on Factors of 35

**List all the factors of 35**1, 5, 7, and 35 are the 35 factors.

**What are the composite factors of 35?**35 is the only composite number in the factors of 35. Composite factors are those that have more than 2 factors other than 1 and itself.

**What are the factors of 35 in pairs?**(1, 35) and (5, 7) are the 35 factors of pairs.

**What are the positive factors for 35?**1, 5, 7, and 35 are the positive factors for 35.

**What are the negative factors of 35?**-1, -5, -7, and -35 are the negative factors of 35.

Now we have closely examined all the important facts and information about the factors of 35. We hope you found this blog to be useful, as well as, easy to understand.

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Written by

Prerit Jain