1. Steps to find factors of 98 using Division Method

Example: Find factors of 98

  • Divide 98 by 1: 98 ÷ 1 : Remainder = 0
  • Divide 98 by 2: 98 ÷ 2 : Remainder = 0
  • Divide 98 by 7: 98 ÷ 7 : Remainder = 0
  • Divide 98 by 14: 98 ÷ 14 : Remainder = 0
  • Divide 98 by 49: 98 ÷ 49 : Remainder = 0
  • Divide 98 by 98: 98 ÷ 98 : Remainder = 0

Hence, Factors of 98 are 1, 2, 7, 14, 49, and 98

2. Steps to find factors of 98 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 98 using the division method, follow these steps:

  • Step 1. Start dividing 98 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 98, which is 2. Divide 98 by 2 to obtain the quotient (49).
    98 ÷ 2 = 49
  • Step 3. Repeat step 1 with the obtained quotient (49).
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 98 is, 98 = 2 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 98 as shown below:

So, the prime factorization of 98 is, 98 = 2 x 7 x 7.

3. Find factors of 98 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 98 would be the two numbers which, when multiplied, give 98 as the result.

The following table represents the calculation of factors of 98 in pairs:

Factor Pair Pair Factorization
1 and 98 1 x 98 = 98
2 and 49 2 x 49 = 98
7 and 14 7 x 14 = 98

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 98. They are called negative pair factors.

Hence, the negative pairs of 98 would be ( -1 , -98 ) , ( -2 , -49 ) and ( -7 , -14 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 98 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, 49, 98 are exact divisors of 98.
  • 1 is a factor of every number. Eg. 1 is a factor of 98.
  • Every number is a factor of zero (0), since 98 x 0 = 0.

Frequently Asked Questions

  • What is prime factorization of 98?

    Prime factorization of 98 is 2 x 7 x 7.

  • How do you find factors of a negative number? ( eg. -98 )?

    Factors of -98 are -1, -2, -7, -14, -49, -98.

  • What are the prime factors of 98?

    The factors of 98 are 1, 2, 7, 14, 49, 98.
    Prime factors of 98 are 2, 7, 7.

  • What are pair factors of 98?

    The pair factors of 98 are (1,98), (2,49), (7,14).

  • What is the greatest prime factors of 98?

    The greatest prime factor of 98 is 7.

  • What are six multiples of 98?

    First five multiples of 98 are 196, 294, 392, 490, 588, 686.

  • What are factors of 98?

    Factors of 98 are 1, 2, 7, 14, 49, 98.

  • Which is the smallest prime factor of 98?

    Smallest prime factor of 98 is 2.

  • Is 98 a whole number?

    Yes 98 is a whole number.

Examples of Factors

Kevin has been asked to write 5 factor(s) of 98. Can you predict the answer?

5 factor(s) of 98 are 1, 2, 7, 14, 49.

Sammy is puzzled while calculating the prime factors of 98. Can you help him find them?

Factors of 98 are 1, 2, 7, 14, 49, 98.
Prime factors of 98 are 2, 7, 7

What is prime factorization of 98?

Prime factorization of 98 is 2 x 7 x 7 = 2 x 72.

Ariel has been assigned the task to find the product of all the prime factors of 98. Can you help her?

Prime factors of 98 are 2, 7, 7.
Hence, the product of prime factors of 14.

Can you help Rubel to find out the product of the even factors of 98?

Factors of 98 are 1, 2, 7, 14, 49, 98.
Even factors of 98 are 2, 14, 98.
Hence, product of even factors of 98 is; 2 x 14 x 98 = 2744.

Joy wants to calculate mean of all the factors of 98. Help him in finding the mean of 98.

Factors of 98 are 1, 2, 7, 14, 49, 98.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 98 is 1 + 2 + 7 + 14 + 49 + 98 = 171.
Hence, the mean of factors of 98 is 171 ÷ 6 = 28.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 98? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 49, 98.
Negative factors are -1, -2, -7, -14, -49, -98.