A day full of math games & activities. Find one near you.

HCF of 404 and 96

HCF of 404 and 96 is the largest possible number that divides 404 and 96 exactly without any remainder. The factors of 404 and 96 are 1, 2, 4, 101, 202, 404 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the HCF of 404 and 96 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 404 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 404 and 96?

Answer: HCF of 404 and 96 is 4.

Explanation:

The HCF of two non-zero integers, x(404) and y(96), is the highest positive integer m(4) that divides both x(404) and y(96) without any remainder.

Methods to Find HCF of 404 and 96

The methods to find the HCF of 404 and 96 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 404 and 96 by Long Division

HCF of 404 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 404 (larger number) by 96 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (96) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 404 and 96.

HCF of 404 and 96 by Prime Factorization

Prime factorization of 404 and 96 is (2 × 2 × 101) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 404 and 96 have common prime factors. Hence, the HCF of 404 and 96 is 2 × 2 = 4.

HCF of 404 and 96 by Listing Common Factors

Factors of 404: 1, 2, 4, 101, 202, 404
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 3 common factors of 404 and 96, that are 1, 2, and 4. Therefore, the highest common factor of 404 and 96 is 4.

☛ Also Check:

HCF of 404 and 96 Examples

Example 1: For two numbers, HCF = 4 and LCM = 9696. If one number is 404, find the other number.

Solution:

Given: HCF (z, 404) = 4 and LCM (z, 404) = 9696
∵ HCF × LCM = 404 × (z)
⇒ z = (HCF × LCM)/404
⇒ z = (4 × 9696)/404
⇒ z = 96
Therefore, the other number is 96.
Example 2: Find the HCF of 404 and 96, if their LCM is 9696.

Solution:

∵ LCM × HCF = 404 × 96
⇒ HCF(404, 96) = (404 × 96)/9696 = 4
Therefore, the highest common factor of 404 and 96 is 4.
Example 3: Find the highest number that divides 404 and 96 exactly.

Solution:

The highest number that divides 404 and 96 exactly is their highest common factor, i.e. HCF of 404 and 96.
⇒ Factors of 404 and 96:
- Factors of 404 = 1, 2, 4, 101, 202, 404
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the HCF of 404 and 96 is 4.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 404 and 96

What is the HCF of 404 and 96?

The HCF of 404 and 96 is 4. To calculate the HCF (Highest Common Factor) of 404 and 96, we need to factor each number (factors of 404 = 1, 2, 4, 101, 202, 404; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the highest factor that exactly divides both 404 and 96, i.e., 4.

What is the Relation Between LCM and HCF of 404, 96?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 404 and 96, i.e. HCF × LCM = 404 × 96.

What are the Methods to Find HCF of 404 and 96?

There are three commonly used methods to find the HCF of 404 and 96.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 404 and 96 by Prime Factorization?

To find the HCF of 404 and 96, we will find the prime factorization of the given numbers, i.e. 404 = 2 × 2 × 101; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 404 and 96. Hence, HCF(404, 96) = 2 × 2 = 4
☛ Prime Numbers

If the HCF of 96 and 404 is 4, Find its LCM.

HCF(96, 404) × LCM(96, 404) = 96 × 404
Since the HCF of 96 and 404 = 4
⇒ 4 × LCM(96, 404) = 38784
Therefore, LCM = 9696
☛ HCF Calculator

How to Find the HCF of 404 and 96 by Long Division Method?

To find the HCF of 404, 96 using long division method, 404 is divided by 96. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum