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HCF of 15 and 35

HCF of 15 and 35 is the largest possible number that divides 15 and 35 exactly without any remainder. The factors of 15 and 35 are 1, 3, 5, 15 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the HCF of 15 and 35 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 15 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 15 and 35?

Answer: HCF of 15 and 35 is 5.

Explanation:

The HCF of two non-zero integers, x(15) and y(35), is the highest positive integer m(5) that divides both x(15) and y(35) without any remainder.

Methods to Find HCF of 15 and 35

The methods to find the HCF of 15 and 35 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 15 and 35 by Prime Factorization

Prime factorization of 15 and 35 is (3 × 5) and (5 × 7) respectively. As visible, 15 and 35 have only one common prime factor i.e. 5. Hence, the HCF of 15 and 35 is 5.

HCF of 15 and 35 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 15 and 35, that are 1 and 5. Therefore, the highest common factor of 15 and 35 is 5.

HCF of 15 and 35 by Long Division

HCF of 15 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 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 15 and 35.

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HCF of 15 and 35 Examples

Example 1: The product of two numbers is 525. If their HCF is 5, what is their LCM?

Solution:

Given: HCF = 5 and product of numbers = 525
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 525/5
Therefore, the LCM is 105.
Example 2: Find the HCF of 15 and 35, if their LCM is 105.

Solution:

∵ LCM × HCF = 15 × 35
⇒ HCF(15, 35) = (15 × 35)/105 = 5
Therefore, the highest common factor of 15 and 35 is 5.
Example 3: For two numbers, HCF = 5 and LCM = 105. If one number is 15, find the other number.

Solution:

Given: HCF (y, 15) = 5 and LCM (y, 15) = 105
∵ HCF × LCM = 15 × (y)
⇒ y = (HCF × LCM)/15
⇒ y = (5 × 105)/15
⇒ y = 35
Therefore, the other number is 35.

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FAQs on HCF of 15 and 35

What is the HCF of 15 and 35?

The HCF of 15 and 35 is 5. To calculate the Highest common factor of 15 and 35, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 35 = 1, 5, 7, 35) and choose the highest factor that exactly divides both 15 and 35, i.e., 5.

What is the Relation Between LCM and HCF of 15, 35?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 15 and 35, i.e. HCF × LCM = 15 × 35.

How to Find the HCF of 15 and 35 by Prime Factorization?

To find the HCF of 15 and 35, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 35 = 5 × 7.
⇒ Since 5 is the only common prime factor of 15 and 35. Hence, HCF (15, 35) = 5.
☛ What are Prime Numbers?

What are the Methods to Find HCF of 15 and 35?

There are three commonly used methods to find the HCF of 15 and 35.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the HCF of 15 and 35 by Long Division Method?

To find the HCF of 15, 35 using long division method, 35 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

If the HCF of 35 and 15 is 5, Find its LCM.

HCF(35, 15) × LCM(35, 15) = 35 × 15
Since the HCF of 35 and 15 = 5
⇒ 5 × LCM(35, 15) = 525
Therefore, LCM = 105
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