Factors of 289
The number 289 is also an odd composite number. The factors of 289 are the numbers which on multiplication in pairs give the product as 289. In this lesson, we will calculate the factors of 289, prime factors of 289, and factors of 289 in pairs along with solved examples for a better understanding.
- Factors of 289: 1, 17, and 289.
- Prime Factorization of 289: 289 = 172
What are the Factors of 289?
Let us recall the meaning of the term 'factor'.
- A factor is a number that divides into another number completely without leaving any remainder.
- Factors of 289 are the numbers which when multiplied together result in 289
- Factors of 289 are 1, 17, and 289.
Let us see how to calculate the factors of 289.
How to Calculate the Factors of 289?
Various methods such as prime factorization and the division method can be used to calculate the factors of 289. In prime factorization, we express 289 as a product of its prime factors and in the division method, we see what numbers divide 289 exactly without a remainder. Hence, the factors of 289 are 1, 17, and 289.
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 289 by Prime Factorization
Prime factorization means expressing a number in terms of the product of its prime factors. We can do use the division method or factor tree to do this.
1. Prime Factorization by Division method
The number 289 is divided by the smallest prime number which divides 289 exactly, i.e. it leaves a remainder 0. The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient becomes indivisible. Since 289 is odd, it will not be divisible by 2 and its multiples. Since the last digit is 9, 289 is divisible by 17
Let us divide 289 by the prime number 17
289 ÷ 17 = 17
17 is again odd, let's again divide by 17
17 ÷ 17 = 1
Now, we got 1 and hence can't be further divided. Prime factorization of 289 = 17 × 17
2. Prime Factorization by Factor Tree
The other way of prime factorization as taking 289 as the root, we create branches by dividing it by prime numbers. This method is similar to above division method. The difference lies in presenting the factorization.
The figure below shows the factor tree of 289. The composite numbers will have branches as they are further divisible. We continue making branches till we are left with only prime numbers.
The numbers inside the circles are the prime factors of 289. Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed it, for prime numbers, there are no other factors.
Factors of 289 in Pairs
The factor pairs of a number are the two numbers which, when multiplied, give the required number.
Considering the number 289, we have
- 1 × 289 = 289
- 17 × 17 = 289
So, the factor pairs of 289 are : (1, 289), (17, 17). The product of two negative numbers also results in a positive number i.e. (-ve) × (-ve) = (+ve).
So, (-1, -289), (-17, -17) are also factor pairs of 289.
Important Notes:
- Every number has a finite number of factors. Factors of 289 have an odd number of factors.
- The factors of 289 are 1, 17, and 289.
- The smallest factor of a number is 1 and the greatest factor of a number would be the number itself
Challenging Questions:
- Is 289 a perfect square number?
- Do the numbers 289 and 0.289 have a common factor?
FAQs on Factors of 289
What are the factors factors of 289?
The factors of 289 are 1, 17, and 289.
Is 289 a prime or composite?
289 is a composite number as it has more than two factors.
What are the prime factors of 289?
The prime factors of 289 is 17.
Are all the factors of 289 prime?
No, all the factors of 289 are not prime.
What is the highest factor of 289?
The highest factor of 289 is 289.