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Factors

Factors of 98 in Pairs | Prime Factorization, Factor Tree of 98

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 98 in Pairs | Prime Factorization, Factor Tree of 98

Factors of 98 in Pairs | Prime Factorization, Factor Tree of 98

Factors of 98 are the numbers that divide the number 98 without leaving any remainder. Since 98 is a composite number, it has multiple factors. There are a total of 6 factors for the number 98, where 98 is the biggest factor. The factors of 98 are both negative and positive. Let us discuss everything about how to find factors of 98 and much more. Scroll down to find out more.

What Are the Factors of 98?

There are a total of 6 factors for the number 98, which doesn’t leave any remainder after division. As discussed above, 98 is not a prime number. Hence, it has more than 2 factors. The positive and negative factors of 98 are given below:

1. The positive factors of 98 are 1, 2, 7, 14, 49, and 98
2. The negative factors of 98 are -1,-2,-7, -14, -49, and -98
3. The prime factors of 98 are 2, 7
4. The prime factorizations of 98 are 2 × 72
5. The sum of prime factors of 98 is 171

Factors of 98 in Pairs

As we said above, there are 6 factors for the number 98. The factors of 98 have both positive and negative pairs. Let us see the positive pair and the negative pair of factors of 98:

Positive Pair Factors of 98

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

Positive Pair Factors of 98

Negative Pair Factors of 98

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

Negative Pair Factors of 98

How To Find Factors of 98 by Division method?

We can also use the division method to figure out the 98 factors. Since 98 is the biggest number, dividing 98 with the sequence of natural numbers till 98 is difficult. Hence, we can divide the number 98 by 2, which is 49. Any number after 49 is not divisible by 98 and leaves the remainder. Therefore, we can divide the number 98 until 49.

  • 98 ÷ 1 = 98
  • 98 ÷ 2 = 49
  • 98 ÷ 3 = can’t be divided (Leaves Remainder)
  • 98 ÷ 4 = can’t be divided (Leaves Remainder)
  • 98 ÷ 5 = can’t be divided (Leaves Remainder)
  • 98 ÷ 6 = can’t be divided (Leaves Remainder)
  • 98 ÷ 7 = 14
  • 98 ÷ 14 = 7
  • 98 ÷ 98 = 1

Hence from the above calculation, we can conclude that 1, 2, 7, 14, 49, and 98 are the factors of 98.

What Is the Prime Factorization of 98?

Since 98 is a composite number, it has more than one prime factor. To find the prime factors of 98, we will use Prime Factorisation. The detailed steps on how to find prime factors of 98 using the prime factorization method are given below:

  • Step 1: Firstly, we will divide 98 by 2 as it’s the smallest prime number.
    • 98 ÷ 2 = 49
  • Step 2: Now, since we cannot divide 49 by 2, we will have to use the next smallest prime number that is divisible by 49. The next smallest prime number which is divisible by 49 is 7.
    • 49 ÷ 7 = 7
  • Step 3: Since 7 can only be divided by 7, we will divide it by 7.
    • 7 ÷ 7 = 1

Therefore, we obtained 1 at the end. This says that prime factors of 98 are 2 x 7 x 7 = 2 x 72. And 2 and 7 are prime numbers of 98.

Prime Factorization of 98

How To Draw a Factor Tree of 98?

In order to find the prime factors of 98, we need to draw the factor tree of 98. The detailed steps on how to draw the factor tree of 98 is given below:

  • Step 1: Firstly, write the number 98 at the top of the factor tree.
  • Step 2: Now, as the tree’s branches, write down the pair factor of 98 that can divide 98. The pair factor we have used here is 2 and 49.
  • Step 3: As we can see, 2 is a prime number, so it cannot be divided. We will circle 2 and move on to 49, which is not a prime number.
  • Step 4: Now, we will divide 49 by the pair factors it is divisible by, which is 7, 7.
  • Step 5: Since 7 is a prime number and has factors 1,7 as their factors, we cannot divide it further.

Hence, circling all the branches gives us factors 2, 7, and 7. Therefore, the prime factors of 98 using a factor tree are 2 X 7 X 7 = 98.

The factor tree of 98 is given below:

Factor tree of 98

Solved Examples on Factors of 98

The solved examples of factors of 98 are given below:

What is the sum of all the factors of 98?
To find the sum of all the factors of 98, we need to add all the factors of 98.
Adding 1 + 2 + 7 + 14 + 49 + 98 = 171.
Hence, the sum of all the factors of 98 is 171.

What are the factors of 98?
Since 98 is a composite number, it has more than two factors. The factor of 98 can be found using the division method.
Hence, the factors of 98 are: 1, 2, 7, 14, 49, and 98.
The Prime Factorization of 98 = 2 x 7 x 7 or 2 x 72

What are the factors and prime factors of 98?
The factors of 92 are 1, 2, 7, 14, 49, and 98.
Whereas the prime factors of 98 are 2 and 7.

What’s the highest common factor of 98 and 126?
The factors of 98 are 1, 2, 7 14, 49, and 98.
And the 126 factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
Hence, from the above, the common factors of 98 and 126 are 1, 2, 7, and 14.
The highest common factor between 98 and 126 is 14.

What’s the highest common factor of 98 and 32?
The factors of 98 are 1, 2, 7, 14, 49, and 98.
And the 32 factors are 1, 2, 4, 8, 16, and 32.
If we see the GFC of 98 and 32, 2 is the highest common factor.

What is the difference between the smallest and largest common factors of 42 and 98?
The factors of 98 are 1, 2, 3, 6, 7, 14, 21, and 42.
And the factors of 98 are 1, 2, 7, 14, 49, and 98.
If we see the GFC of 42 and 98, 14 is the highest common factor of 42 and 98.
And the smallest factor between 42 and 98 is 1.
The difference between the smallest and largest common factors of 42 and 98 is 13.
14 – 1 = 13

FAQs on Prime Factors of 98

The frequently asked questions on prime factors of 98 are given below:

What are the greatest common factors between 100 and 98?
The GFC of 100 and 98, 2 is the highest common factor.

What are the composite factors of 98?
Composite numbers are those that are described as whole digits and have three or more whole number factors.
14, 49, and 98 are the composite factors of 98.

What factors of 98 are perfect squares?
1 and 49 are the perfect squares of factors of 98.

What are the pair factors of 98?
(1, 98), (2, 49), and (7, 14) are the pair factors of 98.

What are the positive factors of 98?
1, 2, 7, 14, 49, and 98 are the positive factors for 98.

What are the factors of -98?
-1, -2, -7, -14, -49, and -98 are the factors of -98.

Conclusion

That concludes the topic of factors and the prime factors of 98. We hope that this information has been helpful to you and that you are now able to easily find the factors of 98 and apply all of the methods. Feel free to leave a comment below if you have any questions or concerns regarding this topic. We will get back to you as soon as possible. 

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