Factors of 97
Factors of 97 are the numbers which when multiplied in pairs give the product as 97. Like all prime numbers, the only factors of 97 are 1 and 97 itself. Factors of 97 can be positive and negative as well. In this lesson, we will calculate the factors of 97, prime factors of 97, and factors of 97 in pairs along with solved examples for a better understanding.
- Factors of 97: 1 and 97
- Prime Factorization of 97: 97 = 1 × 97
What are the Factors of 97?
The factor of a number is that number which divides it completely i.e., leaving no remainder. For example: To find the factors of the number 97, we will have to perform division on 97 and find the numbers which divide 97 completely, leaving no remainders. The factors of 97 are the numbers that exactly divide 97. Since 97 is a prime number, it has only two factors, they are 1 and 97
How to Calculate the Factors of 97?
To calculate the factors of any number, here in this case 97, we need to find all the numbers that would divide 97 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, etc up to 97 respectively. The number 1 and the number itself would always be a factor of the given number. Refer to the following table to check division 97 by its factors:
| S.No. | Division | Factor |
|---|---|---|
| 1. | 97/1 |
Remainder = 0 Factor = 1 |
| 2. | 97/97 |
Remainder = 0 Factor = 97 |
97 is a prime number since it has only two factors 1 and 97. A composite number has more than two factors.
Explore factors using illustrations and interactive examples.
- Factors of 120 - The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 60 - The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 97 by Prime Factorization
Prime Factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors.
Method 1. Division Method
To find prime factors of 97 using the division method,
- Step1. Start dividing 97 from the smallest prime number i.e., 2, 3, 5, and so on. and find the smallest prime factor of the number.
- Step2. After finding the smallest prime factor of the number 97 i.e., 97 itself, divide 97 by 97 to obtain the quotient as 1
- 97/1 = 1
- So, the prime factorization of 97 is: 97 = 97 × 1
Method 2. Factor Tree Method
We can conduct the same procedure using the factor tree as shown in the diagram given below:
So, the Prime factorization of 97 is 97 = 97 × 1
Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus, the total factors can be written including both the prime and composite numbers together as,1, 97
Factors of 97 in Pairs
Pair factors are the factors of a number given in pairs when multiplied together give that original number. The pair factors of 97 would be the two numbers when multiplied together, result in the value 97. The following table represents the calculation of pair factors of 97:
| S.No. | Positive Factor Pair | Negative Factor Pair | Pair Factorization |
|---|---|---|---|
| 1. | 1 and 97 | -1 and -97 |
1 × 97 = 97 |
Important Notes:
- Only whole numbers and integers can be converted into factors.
- Only composite numbers can have more than two factors.
- The smallest factor of a number is 1 and the biggest factor of a number is the number itself.
Challenging Questions:
- Twin primes are a pair of prime numbers that have a difference of 2. How many pairs of twin primes are there between 1 and 97?
FAQs on Factors of 97
What are the factors of 97?
Factors of 97 are 1, and 97
Is 97 a prime or composite?
97 is a prime number as it has only two factors, 1 and 97
What are the common factors of 97 and 43?
Factors of 97 = 1, and 97
Factors of 43 = 1, and 43
The common factor of 97 and 43 is 1
What are the common factors of 97 and 100?
Factors of 97 = 1, and 97
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50 and 100.
The common factor of 97 and 100 is 1
What are the common factors of 97 and 72?
Factors of 97 = 1, and 97
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
The common factor of 97 and 72 is 1