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HCF of 14 and 35

HCF of 14 and 35 is the largest possible number that divides 14 and 35 exactly without any remainder. The factors of 14 and 35 are 1, 2, 7, 14 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the HCF of 14 and 35 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 14 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 14 and 35?

Answer: HCF of 14 and 35 is 7.

Explanation:

The HCF of two non-zero integers, x(14) and y(35), is the highest positive integer m(7) that divides both x(14) and y(35) without any remainder.

Methods to Find HCF of 14 and 35

The methods to find the HCF of 14 and 35 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 14 and 35 by Long Division

HCF of 14 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the HCF of 14 and 35.

HCF of 14 and 35 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 35 and Y = 14

HCF(35, 14) = HCF(14, 35 mod 14) = HCF(14, 7)
HCF(14, 7) = HCF(7, 14 mod 7) = HCF(7, 0)
HCF(7, 0) = 7 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 14 and 35 is 7.

HCF of 14 and 35 by Prime Factorization

Prime factorization of 14 and 35 is (2 × 7) and (5 × 7) respectively. As visible, 14 and 35 have only one common prime factor i.e. 7. Hence, the HCF of 14 and 35 is 7.

☛ Also Check:

HCF of 14 and 35 Examples

Example 1: For two numbers, HCF = 7 and LCM = 70. If one number is 14, find the other number.

Solution:

Given: HCF (y, 14) = 7 and LCM (y, 14) = 70
∵ HCF × LCM = 14 × (y)
⇒ y = (HCF × LCM)/14
⇒ y = (7 × 70)/14
⇒ y = 35
Therefore, the other number is 35.
Example 2: Find the highest number that divides 14 and 35 exactly.

Solution:

The highest number that divides 14 and 35 exactly is their highest common factor, i.e. HCF of 14 and 35.
⇒ Factors of 14 and 35:
- Factors of 14 = 1, 2, 7, 14
- Factors of 35 = 1, 5, 7, 35
Therefore, the HCF of 14 and 35 is 7.
Example 3: Find the HCF of 14 and 35, if their LCM is 70.

Solution:

∵ LCM × HCF = 14 × 35
⇒ HCF(14, 35) = (14 × 35)/70 = 7
Therefore, the highest common factor of 14 and 35 is 7.

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FAQs on HCF of 14 and 35

What is the HCF of 14 and 35?

The HCF of 14 and 35 is 7. To calculate the HCF (Highest Common Factor) of 14 and 35, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 35 = 1, 5, 7, 35) and choose the highest factor that exactly divides both 14 and 35, i.e., 7.

How to Find the HCF of 14 and 35 by Long Division Method?

To find the HCF of 14, 35 using long division method, 35 is divided by 14. The corresponding divisor (7) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 14 and 35?

There are three commonly used methods to find the HCF of 14 and 35.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and HCF of 14, 35?

The following equation can be used to express the relation between Least Common Multiple and HCF of 14 and 35, i.e. HCF × LCM = 14 × 35.

How to Find the HCF of 14 and 35 by Prime Factorization?

To find the HCF of 14 and 35, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 35 = 5 × 7.
⇒ Since 7 is the only common prime factor of 14 and 35. Hence, HCF (14, 35) = 7.
☛ Prime Numbers

If the HCF of 35 and 14 is 7, Find its LCM.

HCF(35, 14) × LCM(35, 14) = 35 × 14
Since the HCF of 35 and 14 = 7
⇒ 7 × LCM(35, 14) = 490
Therefore, LCM = 70
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