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HCF of 35 and 40

HCF of 35 and 40 is the largest possible number that divides 35 and 40 exactly without any remainder. The factors of 35 and 40 are 1, 5, 7, 35 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the HCF of 35 and 40 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 35 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 35 and 40?

Answer: HCF of 35 and 40 is 5.

Explanation:

The HCF of two non-zero integers, x(35) and y(40), is the highest positive integer m(5) that divides both x(35) and y(40) without any remainder.

Methods to Find HCF of 35 and 40

Let's look at the different methods for finding the HCF of 35 and 40.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 35 and 40 by Prime Factorization

Prime factorization of 35 and 40 is (5 × 7) and (2 × 2 × 2 × 5) respectively. As visible, 35 and 40 have only one common prime factor i.e. 5. Hence, the HCF of 35 and 40 is 5.

HCF of 35 and 40 by Listing Common Factors

Factors of 35: 1, 5, 7, 35
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 2 common factors of 35 and 40, that are 1 and 5. Therefore, the highest common factor of 35 and 40 is 5.

HCF of 35 and 40 by Long Division

HCF of 35 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 35 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 35 and 40.

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HCF of 35 and 40 Examples

Example 1: The product of two numbers is 1400. If their HCF is 5, what is their LCM?

Solution:

Given: HCF = 5 and product of numbers = 1400
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1400/5
Therefore, the LCM is 280.
Example 2: Find the HCF of 35 and 40, if their LCM is 280.

Solution:

∵ LCM × HCF = 35 × 40
⇒ HCF(35, 40) = (35 × 40)/280 = 5
Therefore, the highest common factor of 35 and 40 is 5.
Example 3: For two numbers, HCF = 5 and LCM = 280. If one number is 40, find the other number.

Solution:

Given: HCF (y, 40) = 5 and LCM (y, 40) = 280
∵ HCF × LCM = 40 × (y)
⇒ y = (HCF × LCM)/40
⇒ y = (5 × 280)/40
⇒ y = 35
Therefore, the other number is 35.

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FAQs on HCF of 35 and 40

What is the HCF of 35 and 40?

The HCF of 35 and 40 is 5. To calculate the Highest common factor of 35 and 40, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the highest factor that exactly divides both 35 and 40, i.e., 5.

If the HCF of 40 and 35 is 5, Find its LCM.

HCF(40, 35) × LCM(40, 35) = 40 × 35
Since the HCF of 40 and 35 = 5
⇒ 5 × LCM(40, 35) = 1400
Therefore, LCM = 280
☛ HCF Calculator

What are the Methods to Find HCF of 35 and 40?

There are three commonly used methods to find the HCF of 35 and 40.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and HCF of 35, 40?

The following equation can be used to express the relation between Least Common Multiple and HCF of 35 and 40, i.e. HCF × LCM = 35 × 40.

How to Find the HCF of 35 and 40 by Prime Factorization?

To find the HCF of 35 and 40, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 40 = 2 × 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 35 and 40. Hence, HCF (35, 40) = 5.
☛ What is a Prime Number?

How to Find the HCF of 35 and 40 by Long Division Method?

To find the HCF of 35, 40 using long division method, 40 is divided by 35. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

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