1. Steps to find factors of 714 using Division Method

Example: Find factors of 714

  • Divide 714 by 1: 714 ÷ 1 : Remainder = 0
  • Divide 714 by 2: 714 ÷ 2 : Remainder = 0
  • Divide 714 by 3: 714 ÷ 3 : Remainder = 0
  • Divide 714 by 6: 714 ÷ 6 : Remainder = 0
  • Divide 714 by 7: 714 ÷ 7 : Remainder = 0
  • Divide 714 by 14: 714 ÷ 14 : Remainder = 0
  • Divide 714 by 17: 714 ÷ 17 : Remainder = 0
  • Divide 714 by 21: 714 ÷ 21 : Remainder = 0
  • Divide 714 by 34: 714 ÷ 34 : Remainder = 0
  • Divide 714 by 42: 714 ÷ 42 : Remainder = 0
  • Divide 714 by 51: 714 ÷ 51 : Remainder = 0
  • Divide 714 by 102: 714 ÷ 102 : Remainder = 0
  • Divide 714 by 119: 714 ÷ 119 : Remainder = 0
  • Divide 714 by 238: 714 ÷ 238 : Remainder = 0
  • Divide 714 by 357: 714 ÷ 357 : Remainder = 0
  • Divide 714 by 714: 714 ÷ 714 : Remainder = 0

Hence, Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, and 714

2. Steps to find factors of 714 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 714 using the division method, follow these steps:

  • Step 1. Start dividing 714 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 714, which is 2. Divide 714 by 2 to obtain the quotient (357).
    714 ÷ 2 = 357
  • Step 3. Repeat step 1 with the obtained quotient (357).
    357 ÷ 3 = 119
    119 ÷ 7 = 17
    17 ÷ 17 = 1

So, the prime factorization of 714 is, 714 = 2 x 3 x 7 x 17.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 714 as shown below:

So, the prime factorization of 714 is, 714 = 2 x 3 x 7 x 17.

3. Find factors of 714 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 714 would be the two numbers which, when multiplied, give 714 as the result.

The following table represents the calculation of factors of 714 in pairs:

Factor Pair Pair Factorization
1 and 714 1 x 714 = 714
2 and 357 2 x 357 = 714
3 and 238 3 x 238 = 714
6 and 119 6 x 119 = 714
7 and 102 7 x 102 = 714
14 and 51 14 x 51 = 714
17 and 42 17 x 42 = 714
21 and 34 21 x 34 = 714

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 714. They are called negative pair factors.

Hence, the negative pairs of 714 would be ( -1 , -714 ) , ( -2 , -357 ) , ( -3 , -238 ) , ( -6 , -119 ) , ( -7 , -102 ) , ( -14 , -51 ) , ( -17 , -42 ) and ( -21 , -34 ) .

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. 714 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, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714 are exact divisors of 714.
  • 1 is a factor of every number. Eg. 1 is a factor of 714.
  • Every number is a factor of zero (0), since 714 x 0 = 0.

Frequently Asked Questions

  • What are the prime factors of 714?

    The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.
    Prime factors of 714 are 2, 3, 7, 17.

  • What two numbers make 714?

    Two numbers that make 714 are 2 and 357.

  • What is the greatest prime factors of 714?

    The greatest prime factor of 714 is 17.

  • What are factors of 714?

    Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.

  • How do you find factors of a negative number? ( eg. -714 )?

    Factors of -714 are -1, -2, -3, -6, -7, -14, -17, -21, -34, -42, -51, -102, -119, -238, -357, -714.

  • What are five multiples of 714?

    First five multiples of 714 are 1428, 2142, 2856, 3570, 4284.

  • Write some multiples of 714?

    First five multiples of 714 are 1428, 2142, 2856, 3570.

  • Is 714 a perfect square?

    No 714 is not a perfect square.

  • What two numbers make 714?

    Two numbers that make 714 are 2 and 357.

Examples of Factors

What is prime factorization of 714?

Prime factorization of 714 is 2 x 3 x 7 x 17 = 2 x 3 x 7 x 17.

Sammy is puzzled while calculating the prime factors of 714. Can you help him find them?

Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.
Prime factors of 714 are 2, 3, 7, 17

Kevin has been asked to write 15 factor(s) of 714. Can you predict the answer?

15 factor(s) of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357.

Joey wants to write all the prime factors of 714 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 714 are 2, 3, 7, 17.
So in exponential form it can be written as 2 x 3 x 7 x 17.

How many factors are there for 714?

Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 714? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.
Negative factors are -1, -2, -3, -6, -7, -14, -17, -21, -34, -42, -51, -102, -119, -238, -357, -714.

Can you help Rubel to find out the product of the even factors of 714?

Factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.
Even factors of 714 are 2, 6, 14, 34, 42, 102, 238, 714.
Hence, product of even factors of 714 is; 2 x 6 x 14 x 34 x 42 x 102 x 238 x 714 = 4158271385856.