1. Steps to find factors of 854 using Division Method

Example: Find factors of 854

  • Divide 854 by 1: 854 ÷ 1 : Remainder = 0
  • Divide 854 by 2: 854 ÷ 2 : Remainder = 0
  • Divide 854 by 7: 854 ÷ 7 : Remainder = 0
  • Divide 854 by 14: 854 ÷ 14 : Remainder = 0
  • Divide 854 by 61: 854 ÷ 61 : Remainder = 0
  • Divide 854 by 122: 854 ÷ 122 : Remainder = 0
  • Divide 854 by 427: 854 ÷ 427 : Remainder = 0
  • Divide 854 by 854: 854 ÷ 854 : Remainder = 0

Hence, Factors of 854 are 1, 2, 7, 14, 61, 122, 427, and 854

2. Steps to find factors of 854 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 854 using the division method, follow these steps:

  • Step 1. Start dividing 854 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 854, which is 2. Divide 854 by 2 to obtain the quotient (427).
    854 ÷ 2 = 427
  • Step 3. Repeat step 1 with the obtained quotient (427).
    427 ÷ 7 = 61
    61 ÷ 61 = 1

So, the prime factorization of 854 is, 854 = 2 x 7 x 61.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 854 as shown below:

So, the prime factorization of 854 is, 854 = 2 x 7 x 61.

3. Find factors of 854 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 854 would be the two numbers which, when multiplied, give 854 as the result.

The following table represents the calculation of factors of 854 in pairs:

Factor Pair Pair Factorization
1 and 854 1 x 854 = 854
2 and 427 2 x 427 = 854
7 and 122 7 x 122 = 854
14 and 61 14 x 61 = 854

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 854. They are called negative pair factors.

Hence, the negative pairs of 854 would be ( -1 , -854 ) , ( -2 , -427 ) , ( -7 , -122 ) and ( -14 , -61 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 854 is a factor of itself.
  • 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, 2, 7, 14, 61, 122, 427, 854 are exact divisors of 854.
  • 1 is a factor of every number. Eg. 1 is a factor of 854.
  • Every number is a factor of zero (0), since 854 x 0 = 0.

Frequently Asked Questions

  • What is prime factorization of 854?

    Prime factorization of 854 is 2 x 7 x 61.

  • How do you find factors of a negative number? ( eg. -854 )?

    Factors of -854 are -1, -2, -7, -14, -61, -122, -427, -854.

  • What are the prime factors of 854?

    The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854.
    Prime factors of 854 are 2, 7, 61.

  • What are pair factors of 854?

    The pair factors of 854 are (1,854), (2,427), (7,122), (14,61).

  • What is the greatest prime factors of 854?

    The greatest prime factor of 854 is 61.

  • What are six multiples of 854?

    First five multiples of 854 are 1708, 2562, 3416, 4270, 5124, 5978.

  • What are factors of 854?

    Factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854.

  • Which is the smallest prime factor of 854?

    Smallest prime factor of 854 is 2.

  • Is 854 a whole number?

    Yes 854 is a whole number.

Examples of Factors

Kevin has been asked to write 7 factor(s) of 854. Can you predict the answer?

7 factor(s) of 854 are 1, 2, 7, 14, 61, 122, 427.

Sammy is puzzled while calculating the prime factors of 854. Can you help him find them?

Factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854.
Prime factors of 854 are 2, 7, 61

What is prime factorization of 854?

Prime factorization of 854 is 2 x 7 x 61 = 2 x 7 x 61.

Ariel has been assigned the task to find the product of all the prime factors of 854. Can you help her?

Prime factors of 854 are 2, 7, 61.
Hence, the product of prime factors of 854.

Can you help Rubel to find out the product of the even factors of 854?

Factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854.
Even factors of 854 are 2, 14, 122, 854.
Hence, product of even factors of 854 is; 2 x 14 x 122 x 854 = 2917264.

Joy wants to calculate mean of all the factors of 854. Help him in finding the mean of 854.

Factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 854 is 1 + 2 + 7 + 14 + 61 + 122 + 427 + 854 = 1488.
Hence, the mean of factors of 854 is 1488 ÷ 8 = 186.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 854? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 61, 122, 427, 854.
Negative factors are -1, -2, -7, -14, -61, -122, -427, -854.