1. Steps to find factors of 702 using Division Method

Example: Find factors of 702

  • Divide 702 by 1: 702 ÷ 1 : Remainder = 0
  • Divide 702 by 2: 702 ÷ 2 : Remainder = 0
  • Divide 702 by 3: 702 ÷ 3 : Remainder = 0
  • Divide 702 by 6: 702 ÷ 6 : Remainder = 0
  • Divide 702 by 9: 702 ÷ 9 : Remainder = 0
  • Divide 702 by 13: 702 ÷ 13 : Remainder = 0
  • Divide 702 by 18: 702 ÷ 18 : Remainder = 0
  • Divide 702 by 26: 702 ÷ 26 : Remainder = 0
  • Divide 702 by 27: 702 ÷ 27 : Remainder = 0
  • Divide 702 by 39: 702 ÷ 39 : Remainder = 0
  • Divide 702 by 54: 702 ÷ 54 : Remainder = 0
  • Divide 702 by 78: 702 ÷ 78 : Remainder = 0
  • Divide 702 by 117: 702 ÷ 117 : Remainder = 0
  • Divide 702 by 234: 702 ÷ 234 : Remainder = 0
  • Divide 702 by 351: 702 ÷ 351 : Remainder = 0
  • Divide 702 by 702: 702 ÷ 702 : Remainder = 0

Hence, Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, and 702

2. Steps to find factors of 702 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 702 using the division method, follow these steps:

  • Step 1. Start dividing 702 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 702, which is 2. Divide 702 by 2 to obtain the quotient (351).
    702 ÷ 2 = 351
  • Step 3. Repeat step 1 with the obtained quotient (351).
    351 ÷ 3 = 117
    117 ÷ 3 = 39
    39 ÷ 3 = 13
    13 ÷ 13 = 1

So, the prime factorization of 702 is, 702 = 2 x 3 x 3 x 3 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 702 as shown below:

So, the prime factorization of 702 is, 702 = 2 x 3 x 3 x 3 x 13.

3. Find factors of 702 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 702 would be the two numbers which, when multiplied, give 702 as the result.

The following table represents the calculation of factors of 702 in pairs:

Factor Pair Pair Factorization
1 and 702 1 x 702 = 702
2 and 351 2 x 351 = 702
3 and 234 3 x 234 = 702
6 and 117 6 x 117 = 702
9 and 78 9 x 78 = 702
13 and 54 13 x 54 = 702
18 and 39 18 x 39 = 702
26 and 27 26 x 27 = 702

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 702. They are called negative pair factors.

Hence, the negative pairs of 702 would be ( -1 , -702 ) , ( -2 , -351 ) , ( -3 , -234 ) , ( -6 , -117 ) , ( -9 , -78 ) , ( -13 , -54 ) , ( -18 , -39 ) and ( -26 , -27 ) .

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

  • Each number is a factor of itself. Eg. 702 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, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 are exact divisors of 702.
  • 1 is a factor of every number. Eg. 1 is a factor of 702.
  • Every number is a factor of zero (0), since 702 x 0 = 0.

Frequently Asked Questions

  • Which is the smallest prime factor of 702?

    Smallest prime factor of 702 is 2.

  • Is 702 a perfect square?

    No 702 is not a perfect square.

  • What are five multiples of 702?

    First five multiples of 702 are 1404, 2106, 2808, 3510, 4212.

  • What is prime factorization of 702?

    Prime factorization of 702 is 2 x 3 x 3 x 3 x 13.

  • What are factors of 702?

    Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.

  • How do you find factors of a negative number? ( eg. -702 )?

    Factors of -702 are -1, -2, -3, -6, -9, -13, -18, -26, -27, -39, -54, -78, -117, -234, -351, -702.

  • Is 702 a whole number?

    Yes 702 is a whole number.

  • Which is greatest factor of 702?

    The greatest factor of 702 is 351.

  • What are the prime factors of 702?

    The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.
    Prime factors of 702 are 2, 3, 3, 3, 13.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 702. Can you help her?

Prime factors of 702 are 2, 3, 3, 3, 13.
Hence, the product of prime factors of 78.

Can you help Rubel to find out the product of the even factors of 702?

Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.
Even factors of 702 are 2, 6, 18, 26, 54, 78, 234, 702.
Hence, product of even factors of 702 is; 2 x 6 x 18 x 26 x 54 x 78 x 234 x 702 = 3885692518656.

Joy wants to calculate mean of all the factors of 702. Help him in finding the mean of 702.

Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 702 is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 351 + 702 = 1680.
Hence, the mean of factors of 702 is 1680 ÷ 16 = 105.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 702? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.
Negative factors are -1, -2, -3, -6, -9, -13, -18, -26, -27, -39, -54, -78, -117, -234, -351, -702.

How many factors are there for 702?

Factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702.
So there are in total 16 factors.

Joey wants to write all the prime factors of 702 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 702 are 2, 3, 3, 3, 13.
So in exponential form it can be written as 2 x 33 x 13.

Kevin has been asked to write 15 factor(s) of 702. Can you predict the answer?

15 factor(s) of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351.