What is HCF of 8, 9, and 25?
HCF of 8, 9, and 25 is 1. HCF stands for Highest Common Factor. HCF of 8, 9, and 25 is the largest common factor which can evenly divide 8, 9, and 25. Hence, 1 is the largest common factor of 8, 9, and 25 which can divide them evenly. HCF is also called the Greatest Common Factor(GCF) or Greatest Common Divisor(GCD) is 1. Hence, GCF or GCD of 8, 9 and 25 is 1.
HCF of 8, 9, and 25 Calculator
Try out the following calculator to find the HCF of 8, 9, and 25
How to Find HCF of 8, 9, and 25?
We can find the HCF of 8, 9, and 25 using the following three methods:
- Listing Factors
- Prime Factorization
- Long Division
HCF of 8, 9, and 25 using Listing Factors
In this method, we list all the factors of all the numbers and select the number that is common and the largest factor.
⇒ Factors of 8 are 1, 2, 4, 8
⇒ Factors of 9 are 1, 3, 9
⇒ Factors of 25 are 1, 5, 25
Ast the only factor common for all the given numbers is 1. Hence, the HCF of 8, 9 and 25 is 1.
HCF of 8, 9 and 25 by Prime Factorization
In Prime factorization method we represent each number as the product of two prime factors. Once we have listed all the numbers we then try to find the factors that are common in all the above-mentioned numbers prime factors. The product of all such prime factors is the HCF of the numbers.
Prime Factorization of 8 = 2 × 2 × 2
Prime Factorization of 9 = 3 × 3
Prime Factorization of 25 = 5 × 5
As there are no common prime factors between 8, 9, 25. Hence, the HCF of 8, 9, 25 is 1.
HCF of 8, 9 and 25 by Long Division method
In this method, we can find the HCF of the first 2 numbers with division method and then the HCF of the produced result with the third number. This will give you the result of the HCF of all the 3 numbers.
In long division method we first calculate the HCF of 9 and 25.
- 25 ÷ 9 ⇒ Q = 2, R = 7
- 9 ÷ 7 ⇒ Q = 1, R = 2
- 7 ÷ 2 ⇒ Q = 3, R = 1
- 2 ÷ 1 ⇒ Q = 2, R = 0
Hence, HCF of 9 and 25 is 1
Now, we will find HCF of 1 and 8
- 8 ÷ 1 ⇒ Q = 8, R = 0
Hence, HCF of 1 and 8 is 1
Thus, HCF of 8, 9 and 25 = HCF (HCF of 9 and 25) and 8 = 1
Also, Check
HCF of 8, 9 and 25 Examples
Example 1: Find the HCF of 8, 9 and 25 by listing factors.
Solution:
⇒ Factors of 8 are 1, 2, 4, 8
⇒ Factors of 9 are 1, 3, 9
⇒ Factors of 25 are 1,5,25 As 1 is the only factor common to all 3 numbers the HCF of 8,9 and 25 is 1.
Example 2: Express 8, 9 as the product of Prime factors.
Solution:
8 = 2 × 2 × 2
9 = 3 × 3
Example 3: How do you calculate the HCF of 3 numbers.
Solution:
In this, we can find the HCF of the first 2 numbers and then the HCF of the produced result with the third number. This will give you the result of the HCF of all the 3 numbers.
Practice Questions on HCF of 8, 9 and 25
Q1. Express 9 and 25 as their prime factors.
Q2. Calculate HCF of 8, 9 and 25 by Long division?
Q3. Find the HCF of 8, 9 and 25 using Prime Factorization Method
Q4. Find the largest number which can divide 8, 9 and 25 evenly
HCF of 8, 9 and 25 FAQs
What is the HCF of 8, 9 and 25?
The HCF of 8, 9 and 25 is 1.
What are the factors of 8, 9 and 25.
Factors of 8 are 1,2,4,8
Factors of 9 are 1,3,9
Factors of 25 are 1,5,25
What is the HCF of two Prime Numbers?
As the prime numbers have only 2 factors 1 and itself, the HCF of two or more prime numbers will always 1.
How to calculate HCF of n numbers?
HCF of n numbers can be calculated by calculating the HCF of two numbers at a time and then calculaing the HCF with rest of the numbers and the previous result.
What are Co-Prime Numbers?
The numbers whose common factor is 1 are called co-prime numbers