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HCF of 8, 9 and 25

HCF of 8, 9 and 25 is the largest possible number that divides 8, 9 and 25 exactly without any remainder. The factors of 8, 9 and 25 are (1, 2, 4, 8), (1, 3, 9) and (1, 5, 25) respectively. There are 3 commonly used methods to find the HCF of 8, 9 and 25 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 8, 9 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 8, 9 and 25?

Answer: HCF of 8, 9 and 25 is 1.

Explanation:

The HCF of three non-zero integers, x(8), y(9) and z(25), is the highest positive integer m(1) that divides x(8), y(9) and z(25) without any remainder.

Methods to Find HCF of 8, 9 and 25

The methods to find the HCF of 8, 9 and 25 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 8, 9 and 25 by Long Division

HCF of 8, 9 and 25 can be represented as HCF of (HCF of 8, 9) and 25. HCF(8, 9, 25) can be thus calculated by first finding HCF(8, 9) using long division and thereafter using this result with 25 to perform long division again.

Step 1: Divide 9 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (1). Repeat this process until the remainder = 0.
⇒ HCF(8, 9) = 1.
Step 3: Now to find the HCF of 1 and 25, we will perform a long division on 25 and 1.
Step 4: For remainder = 0, divisor = 1 ⇒ HCF(1, 25) = 1

Thus, HCF(8, 9, 25) = HCF(HCF(8, 9), 25) = 1.

HCF of 8, 9 and 25 by Prime Factorization

Prime factorization of 8, 9 and 25 is (2 × 2 × 2), (3 × 3) and (5 × 5) respectively. As visible, there are no common prime factors between 8, 9 and 25, i.e. they are coprime. Hence, the HCF of 8, 9 and 25 will be 1.

HCF of 8, 9 and 25 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 9: 1, 3, 9
Factors of 25: 1, 5, 25

Since, 1 is the only common factor between 8, 9 and 25. The Highest Common Factor of 8, 9 and 25 is 1.

☛ Also Check:

HCF of 8, 9 and 25 Examples

Example 1: Calculate the HCF of 8, 9, and 25 using LCM of the given numbers.

Solution:

Prime factorization of 8, 9 and 25 is given as,
- 8 = 2 × 2 × 2
- 9 = 3 × 3
- 25 = 5 × 5
LCM(8, 9) = 72, LCM(9, 25) = 225, LCM(25, 8) = 200, LCM(8, 9, 25) = 1800
⇒ HCF(8, 9, 25) = [(8 × 9 × 25) × LCM(8, 9, 25)]/[LCM(8, 9) × LCM (9, 25) × LCM(25, 8)]
⇒ HCF(8, 9, 25) = (1800 × 1800)/(72 × 225 × 200)
⇒ HCF(8, 9, 25) = 1.
Therefore, the HCF of 8, 9 and 25 is 1.
Example 2: Find the highest number that divides 8, 9, and 25 completely.

Solution:

The highest number that divides 8, 9, and 25 exactly is their highest common factor.
- Factors of 8 = 1, 2, 4, 8
- Factors of 9 = 1, 3, 9
- Factors of 25 = 1, 5, 25
The HCF of 8, 9, and 25 is 1.
∴ The highest number that divides 8, 9, and 25 is 1.
Example 3: Verify the relation between the LCM and HCF of 8, 9 and 25.

Solution:

The relation between the LCM and HCF of 8, 9 and 25 is given as, HCF(8, 9, 25) = [(8 × 9 × 25) × LCM(8, 9, 25)]/[LCM(8, 9) × LCM (9, 25) × LCM(8, 25)]
⇒ Prime factorization of 8, 9 and 25:
- 8 = 2 × 2 × 2
- 9 = 3 × 3
- 25 = 5 × 5
∴ LCM of (8, 9), (9, 25), (8, 25), and (8, 9, 25) is 72, 225, 200, and 1800 respectively.
Now, LHS = HCF(8, 9, 25) = 1.
And, RHS = [(8 × 9 × 25) × LCM(8, 9, 25)]/[LCM(8, 9) × LCM (9, 25) × LCM(8, 25)] = [(1800) × 1800]/[72 × 225 × 200]
LHS = RHS = 1.
Hence verified.

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FAQs on HCF of 8, 9 and 25

What is the HCF of 8, 9 and 25?

The HCF of 8, 9 and 25 is 1. To calculate the HCF (Highest Common Factor) of 8, 9 and 25, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 9 = 1, 3, 9; factors of 25 = 1, 5, 25) and choose the highest factor that exactly divides 8, 9 and 25, i.e., 1.

Which of the following is HCF of 8, 9 and 25? 1, 57, 39, 37, 37, 70, 29, 43, 72

HCF of 8, 9, 25 will be the number that divides 8, 9, and 25 without leaving any remainder. The only number that satisfies the given condition is 1.

What is the Relation Between LCM and HCF of 8, 9 and 25?

The following equation can be used to express the relation between Least Common Multiple and HCF of 8, 9 and 25, i.e. HCF(8, 9, 25) = [(8 × 9 × 25) × LCM(8, 9, 25)]/[LCM(8, 9) × LCM (9, 25) × LCM(8, 25)].
☛ Highest Common Factor Calculator

How to Find the HCF of 8, 9 and 25 by Prime Factorization?

To find the HCF of 8, 9 and 25, we will find the prime factorization of given numbers, i.e. 8 = 2 × 2 × 2; 9 = 3 × 3; 25 = 5 × 5.
⇒ There is no common prime factor for 8, 9 and 25. Hence, HCF(8, 9, 25) = 1.
☛ Prime Number

What are the Methods to Find HCF of 8, 9 and 25?

There are three commonly used methods to find the HCF of 8, 9 and 25.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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