Factors of 98
Factors of 98 are integers that can be divided evenly into 98. There are overall 6 factors of 98 among which 98 is the biggest factor and 1, 2, 7, 14, 49 and 98 are positive factors. The Pair Factors of 98 are (1, 98), (2, 49) and (7, 14) and its Prime Factors are 1, 2, 7, 14, 49, 98.
- Factors of 98: 1, 2, 7, 14, 49 and 98
- Negative Factors of 98: -1, -2, -7, -14, -49 and -98
- Prime Factors of 98: 2, 7
- Prime Factorization of 98: 2 × 7 × 7 = 2 × 72
- Sum of Factors of 98: 171
| 1. | What Are the Factors of 98? |
| 2. | Important Notes |
| 3. | How to Calculate the Factors of 98? |
| 4. | Factors of 98 by Prime Factorization |
| 5. | Factors of 98 in Pairs |
| 6. | FAQs on Factors of 98 |
| 7. | Tips and Tricks |
What Are the Factors of 98?
The factor of 98 is any number which on dividing 98 leaves no remainder. Since 98 is a composite number, it has more than two factors. 98 has a total of 6 factors. The Factors of 98 are 1, 2, 7, 14, 49, and 98
Example: We can use division to check whether 2, 7, and 49 are factors of 98. As they leave no remainder, they are indeed the factors of 98.
Important Notes
- Only whole numbers and integers can be factors.
- Only composite numbers can have more than two factors.
- Every factor of a given number is either less than or equal to the given number.
- The number of factors of a given number is finite.
How to Calculate the Factors of 98?
There are two common methods to find the factors of 98.
Method 1: Division method
Method 2: Prime factorization method
Let us calculate factors of 98 using the division method.
In considering numbers that can divide 98 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 49 (which is exactly half of 98).
- 98 ÷1 = 98; 1 and 98 are factors.
- 98 ÷2 = 49; 2 and 49 are factors.
- 98 ÷3 ⇒ is not divisible
- 98 ÷4 ⇒ is not divisible
- 98 ÷5 ⇒ is not divisible
- 98 ÷6 ⇒ is not divisible
- 98 ÷7 = 14; 7 and 14 are factors.
Thus, the factors of 98 are 1, 2, 7, 14, 49, and 98.
Factors of 98 by Prime Factorization
Factorization of a number means writing the number as a product of its factors. Prime Factorization is finding which prime numbers multiply together to make the original number. The prime factors of 98 are written as 2 x 7 x 7, where 2 and 7 are prime numbers.
The same division process is best represented in the form of a factor tree. A factor tree is a special branching diagram where we find the factors of a number, then keep on finding the factors of those numbers until we cannot factor them anymore.
The ends of a factor tree are all the prime factors of the original number as shown in the image
The prime factorization of 98 is written as 2 × 7 × 7 or 2 × 72.
Factors of 98 in pairs
- Pair factors of the number 98 are any two whole numbers (pair) which are multiplied to each other to get the original number, i.e., 98.
- Pair factors could either be positive or negative integers but not a fractional or a decimal number.
| Positive Factor Pairs | Negative Factor Pairs |
|---|---|
| 1 × 98 = 98 ⇒ (1,98) | -1 × -98 = 98 ⇒ (-1,-98) |
| 2 × 49 =98 ⇒ (2,49) | -2 × -49 =98 ⇒ (-2,-49) |
| 7 × 14 = 98 ⇒ (7,14) | -7 × -14 = 98 ⇒ (-7,-14) |
Tips and Tricks
The prime factorization of 98 = 2 x 7 x 7 = 21 x 72
To get the total numbers of factors of 98, simply add one to the exponents and multiply their sums. (1 + 1) x (2 + 1) = 6
Thus, 98 has a total of 6 factors.
FAQs on Factors of 98
What are the Factors of 98?
The factors of 98 are 1, 2, 7, 14, 49, 98 and its negative factors are -1, -2, -7, -14, -49, -98.
What is the Greatest Common Factor of 98 and 16?
The factors of 98 and 16 are 1, 2, 7, 14, 49, 98 and 1, 2, 4, 8, 16 respectively.
Common factors of 98 and 16 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 98 and 16 is 2.
What is the Sum of all the Factors of 98?
Since all factors of 98 are 1, 2, 7, 14, 49, 98 therefore, the sum of its factors is 1 + 2 + 7 + 14 + 49 + 98 = 171.
How Many Factors of 98 are also Factors of 45?
Since, the factors of 98 are 1, 2, 7, 14, 49, 98 and factors of 45 are 1, 3, 5, 9, 15, 45. Hence, 98 and 45 have only one common factor which is 1. Therefore, 98 and 45 are co-prime.
What Numbers are the Prime Factors of 98?
The prime factors of 98 are 2, 7.