Factors

# Factors of 67 | Prime Factorization of 67 | Factor Tree of 67

Written by Prerit Jain

Updated on: 09 Jun 2023

Contents

### Factors of 67 | Prime Factorization of 67 | Factor Tree of 67

## Factors of 67

Factors of 67 | Factor Pairs of 67 | Prime factors of 67 |

1, 67 | (1,67) | 67 |

**Factors of 67**,

**Factor Pairs of 67**,

**Prime factors of 67**

Calculate Factors of

**The Factors are**

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## What are the factors of 67

A factor of a number is a number that can divide the given number evenly. To find the factors of 67, you can divide 67 by each of the numbers that can be evenly divided into it without a remainder and a decimal point in the quotient.

67 is a prime number, which means that it has only two factors: 1 and itself. This means that the only numbers that can be evenly divided into 67 are 1 and 67.

**Thus, the factors of 67 are 1 and 67.**

## How to Find Factors of 67

Here are four methods you can use to find the factors of a number:

- Factors of 67 using the Multiplication Method
- Factors of 67 using the Division Method
- Prime Factorization of 67
- Factor tree of 67

## Factors of 67 Using the Multiplication Method

- To find the factors of 67 using the multiplication method, you can start by listing the numbers from 1 to 67. Then, for each number in the list, you can multiply it by all of the other numbers to see if the product is equal to 67.
- For example, you can start by multiplying 1 by 67. If the product is 67, then 1 and 67 are both factors of 67. You can then move on to the next number in the list and repeat the process.
- Using this method, you will find that the only two numbers that multiply to equal 67 are 1 and 67. Therefore, the factors of 67 using the multiplication method are 1 and 67.

## Factors of 67 Using the Division Method

To find the factors of 67 using the division method, you can start by dividing 67 by each of the numbers that can be evenly divided into it. You can continue this process until you reach a number that 67 cannot be divided by evenly.

For example, if you start by dividing 67 by 1 and the result is an integer (a whole number), then 1 is a factor of 67. You can then move on to the next number in the list and repeat the process.

Using this method, you will find that the only two numbers that 67 can be evenly divided by are 1 and 67. Therefore, the factors of 67 using the division method are 1 and 67.

## Prime Factorization of 67

Calculate Prime Factors of

The Prime Factors of 67 =

67

The prime factorization of 67 is the expression of 67 as the product of its prime factors. Because 67 is a prime number, its prime factorization is simply 67 itself. This means that the prime factorization of 67 is written as 67.

To find the prime factorization of a number, you can express the number as the product of its prime factors. For example, the prime factorization of 15 is 3 x 5, because 15 can be expressed as the product of the prime numbers 3 and 5 (3 x 5 = 15).

The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 67 is written as 67 x 1.

## Factor tree of 67

To create a factor tree for 67, you can start by finding two factors of 67 that multiply to equal 67. Since 67 is a prime number, it only has two factors: 1 and itself.

We can represent these factors as branches on a tree, like this:

67

/

1 67

This shows that 67 can be expressed as the product of 1 and 67. Since 1 and 67 are both prime numbers, we cannot find any other factors for them, so we can stop there. Our final tree would look like this:

67

/

1 67

This is the complete factor tree for 67.

## Factor Pairs of 67

Calculate Pair Factors of

1 x 67=67

So Pair Factors of 67 are

(1,67)

A factor pair of a number is a set of two factors that multiply together to produce that number. For 67, the only factor pair is (1, 67), since these are the only two factors of 67.

The factors of a number are the numbers that can be divided evenly into that number. For 67, the only factors are 1 and 67, since these are the only numbers that can be evenly divided into 67.

In general, the factor pairs of a number can be found by taking all of the factors of that number and pairing them up in all possible combinations. For 67, the only factor pair is (1, 67).

## More Factors

## Factors of 67 – Quick Recap

**Factors of 67:**1, 67.**Negative Factors of 67:**-1, -67.**Prime Factors of 67:**1 and 67**Prime Factorization of 67:**1 and 67

## Factors of 67 – Fun Facts

- 67 is a prime number, which means it has only two factors: 1 and itself. This means that 67 is only divisible by 1 and 67.
- The prime factorization of 67 is 67, which means that 67 is a prime number and cannot be written as the product of any other numbers.
- The sum of the factors of 67 is 68, which is 1 + 67.
- There are no even factors of 67 since 67 is an odd number and can only be divided by odd numbers.
- 67 is not a perfect square, so it does not have any square factors.

**Also Check**: Multiples, Square Root, and LCM

## Solved Examples of Factor of 67

**Q.1: What pairs of numbers multiplied together would equal sixty-seven? ****Solution:** Two numbers which when multiplied together would equal sixty-seven is 1×67; 1×67=67 only.

** Q.2: If you divide sixty-seven by three, what will the remainder be? Solution:** The remainder when dividing sixty-seven by three is one.

** Q.3: How many even numbers remain between one and sixty-seven when all odd numbers are removed? Solution: **Thirty-two even numbers remain between one and sixty-seven when all odd numbers are removed; these would include 2, 4, 6, 8 10, 12 14, 16 18, 20 22, 24 26, 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 & 66.

** Q.4: Find the prime factorization of sixty-seven. Solution:** The prime factorization of sixty-seven is 67 = 67 x 1; both being prime numbers.

** Q.5: Chris needs to multiply three unequal numbers together in order to generate a total of eighty-four, which combination can he use? Solution: **Three number combinations that can be used to multiply together to total eighty-four are 2 x 3 x 14 = 84, 1 x 4 x 21 = 84, and 6 x 7 x 2 = 84.

** Q.6: Find the greatest common factor for twenty-nine and thirty-one. Solution:** The greatest common factor for twenty-nine and thirty-one is one as neither can be divided evenly without a remainder over another number apart from themselves or one (29/31= 0.93548387).

** Q.10:What pair of prime numbers can only be divided evenly with themselves and one in order to produce a total that equals fifty-three? Solution:** Two prime numbers that can only be divided evenly with themselves and one in order to produce a total that equals fifty-three are 53 & 1; 53 x1=53and neither can be divided evenly with another number apart from themselves or one in order to equal fifty-three.

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## Frequently Asked Questions on Factors of 67

**What is the Greatest Common Factor (GCF) of 67?**

The greatest common factor (GCF) of 67 is 1, it’s the largest number which both can be divided without a remainder.

**How many factors does sixty-seven have?**

Sixty-seven has two different factors; these include 1 and 67.

**Is 30 a multiple or a factor of 67?**

30 is not a multiple or factor of sixty-seven as it cannot be divided evenly with no remainder (30/67 = 0.4477611940).

**How many odd numbers remain between 1-67 when all even numbers are removed?**

Thirty-two odd numbers remain between one and sixty-seven when all even numbers are removed; these would include 1, 3, 5, 7, 9 11, 13 15, 17 19, 21 23, 25 27 29, 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 & 67.

**How many pairs of factors are needed in order to multiply together in order to generate fifty-three?**

One pair of factors need multiplying together in order to generate fifty-three; these would include (53,1)

Written by

Prerit Jain