1. Steps to find factors of 667 using Division Method

Example: Find factors of 667

  • Divide 667 by 1: 667 ÷ 1 : Remainder = 0
  • Divide 667 by 23: 667 ÷ 23 : Remainder = 0
  • Divide 667 by 29: 667 ÷ 29 : Remainder = 0
  • Divide 667 by 667: 667 ÷ 667 : Remainder = 0

Hence, Factors of 667 are 1, 23, 29, and 667

2. Steps to find factors of 667 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 667 using the division method, follow these steps:

  • Step 1. Start dividing 667 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 667, which is 23. Divide 667 by 23 to obtain the quotient (29).
    667 ÷ 23 = 29
  • Step 3. Repeat step 1 with the obtained quotient (29).
    29 ÷ 29 = 1

So, the prime factorization of 667 is, 667 = 23 x 29.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 667 as shown below:

So, the prime factorization of 667 is, 667 = 23 x 29.

3. Find factors of 667 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 667 would be the two numbers which, when multiplied, give 667 as the result.

The following table represents the calculation of factors of 667 in pairs:

Factor Pair Pair Factorization
1 and 667 1 x 667 = 667
23 and 29 23 x 29 = 667

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 667. They are called negative pair factors.

Hence, the negative pairs of 667 would be ( -1 , -667 ) , ( -23 , -29 ) .

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of factors

  • Every number is a factor of zero (0), since 667 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 23, 29, 667 are exact divisors of 667.
  • Factors of 667 are 1, 23, 29, 667. Each factor divides 667 without leaving a remainder.

Frequently Asked Questions

  • What are the prime factors of 667?

    The factors of 667 are 1, 23, 29, 667.
    Prime factors of 667 are 23, 29.

  • What is the sum of all factors of 667?

    The sum of all factors of 667 is 720.

  • What are the pair factors of 667?

    Pair factors of 667 are (1,667), (23,29).

  • What two numbers make 667?

    Two numbers that make 667 are 23 and 29.

  • What are multiples of 667?

    First five multiples of 667 are 1334, 2001, 2668, 3335.

  • Is 667 a perfect square?

    No 667 is not a perfect square.

  • Which is greatest factor of 667?

    The greatest factor of 667 is 29.

  • How do you factors of 667?

    Factors of 667 are 1, 23, 29, 667.

  • What are five multiples of 667?

    First five multiples of 667 are 1334, 2001, 2668, 3335, 4002.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 667?

Factors of 667 are 1, 23, 29, 667.
Even factors of 667 are 0.
Hence, product of even factors of 667 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 667? Help her in writing all the factors.

Positive factors are 1, 23, 29, 667.
Negative factors are -1, -23, -29, -667.

How many factors are there for 667?

Factors of 667 are 1, 23, 29, 667.
So there are in total 4 factors.

Sammy is puzzled while calculating the prime factors of 667. Can you help him find them?

Factors of 667 are 1, 23, 29, 667.
Prime factors of 667 are 23, 29

Joey wants to write all the prime factors of 667 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 667 are 23, 29.
So in exponential form it can be written as 23 x 29.

What is prime factorization of 667?

Prime factorization of 667 is 23 x 29 = 23 x 29.

Can you help Rubel to find out the product of the even factors of 667?

Factors of 667 are 1, 23, 29, 667.
Even factors of 667 are 0.
Hence, product of even factors of 667 is; 0 = 0.