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HCF of 35 and 70

HCF of 35 and 70 is the largest possible number that divides 35 and 70 exactly without any remainder. The factors of 35 and 70 are 1, 5, 7, 35 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the HCF of 35 and 70 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 35 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 35 and 70?

Answer: HCF of 35 and 70 is 35.

Explanation:

The HCF of two non-zero integers, x(35) and y(70), is the highest positive integer m(35) that divides both x(35) and y(70) without any remainder.

Methods to Find HCF of 35 and 70

The methods to find the HCF of 35 and 70 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 35 and 70 by Long Division

HCF of 35 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 70 (larger number) by 35 (smaller number).
Step 2: Since the remainder = 0, the divisor (35) is the HCF of 35 and 70.

The corresponding divisor (35) is the HCF of 35 and 70.

HCF of 35 and 70 by Prime Factorization

Prime factorization of 35 and 70 is (5 × 7) and (2 × 5 × 7) respectively. As visible, 35 and 70 have common prime factors. Hence, the HCF of 35 and 70 is 5 × 7 = 35.

HCF of 35 and 70 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 = 70 and Y = 35

HCF(70, 35) = HCF(35, 70 mod 35) = HCF(35, 0)
HCF(35, 0) = 35 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 35 and 70 is 35.

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HCF of 35 and 70 Examples

Example 1: Find the highest number that divides 35 and 70 exactly.

Solution:

The highest number that divides 35 and 70 exactly is their highest common factor, i.e. HCF of 35 and 70.
⇒ Factors of 35 and 70:
- Factors of 35 = 1, 5, 7, 35
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Therefore, the HCF of 35 and 70 is 35.
Example 2: Find the HCF of 35 and 70, if their LCM is 70.

Solution:

∵ LCM × HCF = 35 × 70
⇒ HCF(35, 70) = (35 × 70)/70 = 35
Therefore, the highest common factor of 35 and 70 is 35.
Example 3: For two numbers, HCF = 35 and LCM = 70. If one number is 70, find the other number.

Solution:

Given: HCF (y, 70) = 35 and LCM (y, 70) = 70
∵ HCF × LCM = 70 × (y)
⇒ y = (HCF × LCM)/70
⇒ y = (35 × 70)/70
⇒ y = 35
Therefore, the other number is 35.

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FAQs on HCF of 35 and 70

What is the HCF of 35 and 70?

The HCF of 35 and 70 is 35. To calculate the Highest common factor (HCF) of 35 and 70, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the highest factor that exactly divides both 35 and 70, i.e., 35.

What are the Methods to Find HCF of 35 and 70?

There are three commonly used methods to find the HCF of 35 and 70.

By Listing Common Factors
By Prime Factorization
By Long Division

If the HCF of 70 and 35 is 35, Find its LCM.

HCF(70, 35) × LCM(70, 35) = 70 × 35
Since the HCF of 70 and 35 = 35
⇒ 35 × LCM(70, 35) = 2450
Therefore, LCM = 70
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What is the Relation Between LCM and HCF of 35, 70?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 35 and 70, i.e. HCF × LCM = 35 × 70.

How to Find the HCF of 35 and 70 by Long Division Method?

To find the HCF of 35, 70 using long division method, 70 is divided by 35. The corresponding divisor (35) when remainder equals 0 is taken as HCF.

How to Find the HCF of 35 and 70 by Prime Factorization?

To find the HCF of 35 and 70, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 70 = 2 × 5 × 7.
⇒ Since 5, 7 are common terms in the prime factorization of 35 and 70. Hence, HCF(35, 70) = 5 × 7 = 35
☛ What are Prime Numbers?

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