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HCF of 210 and 55

HCF of 210 and 55 is the largest possible number that divides 210 and 55 exactly without any remainder. The factors of 210 and 55 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 and 1, 5, 11, 55 respectively. There are 3 commonly used methods to find the HCF of 210 and 55 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 210 and 55
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 210 and 55?

Answer: HCF of 210 and 55 is 5.

Explanation:

The HCF of two non-zero integers, x(210) and y(55), is the highest positive integer m(5) that divides both x(210) and y(55) without any remainder.

Methods to Find HCF of 210 and 55

The methods to find the HCF of 210 and 55 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 210 and 55 by Listing Common Factors

Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Factors of 55: 1, 5, 11, 55

There are 2 common factors of 210 and 55, that are 1 and 5. Therefore, the highest common factor of 210 and 55 is 5.

HCF of 210 and 55 by Long Division

HCF of 210 and 55 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 210 (larger number) by 55 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (45).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 210 and 55.

HCF of 210 and 55 by Prime Factorization

Prime factorization of 210 and 55 is (2 × 3 × 5 × 7) and (5 × 11) respectively. As visible, 210 and 55 have only one common prime factor i.e. 5. Hence, the HCF of 210 and 55 is 5.

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HCF of 210 and 55 Examples

Example 1: For two numbers, HCF = 5 and LCM = 2310. If one number is 55, find the other number.

Solution:

Given: HCF (x, 55) = 5 and LCM (x, 55) = 2310
∵ HCF × LCM = 55 × (x)
⇒ x = (HCF × LCM)/55
⇒ x = (5 × 2310)/55
⇒ x = 210
Therefore, the other number is 210.
Example 2: Find the highest number that divides 210 and 55 exactly.

Solution:

The highest number that divides 210 and 55 exactly is their highest common factor, i.e. HCF of 210 and 55.
⇒ Factors of 210 and 55:
- Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
- Factors of 55 = 1, 5, 11, 55
Therefore, the HCF of 210 and 55 is 5.
Example 3: Find the HCF of 210 and 55, if their LCM is 2310.

Solution:

∵ LCM × HCF = 210 × 55
⇒ HCF(210, 55) = (210 × 55)/2310 = 5
Therefore, the highest common factor of 210 and 55 is 5.

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FAQs on HCF of 210 and 55

What is the HCF of 210 and 55?

The HCF of 210 and 55 is 5. To calculate the HCF of 210 and 55, we need to factor each number (factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210; factors of 55 = 1, 5, 11, 55) and choose the highest factor that exactly divides both 210 and 55, i.e., 5.

What are the Methods to Find HCF of 210 and 55?

There are three commonly used methods to find the HCF of 210 and 55.

By Long Division
By Listing Common Factors
By Prime Factorization

If the HCF of 55 and 210 is 5, Find its LCM.

HCF(55, 210) × LCM(55, 210) = 55 × 210
Since the HCF of 55 and 210 = 5
⇒ 5 × LCM(55, 210) = 11550
Therefore, LCM = 2310
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What is the Relation Between LCM and HCF of 210, 55?

The following equation can be used to express the relation between Least Common Multiple and HCF of 210 and 55, i.e. HCF × LCM = 210 × 55.

How to Find the HCF of 210 and 55 by Long Division Method?

To find the HCF of 210, 55 using long division method, 210 is divided by 55. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

How to Find the HCF of 210 and 55 by Prime Factorization?

To find the HCF of 210 and 55, we will find the prime factorization of the given numbers, i.e. 210 = 2 × 3 × 5 × 7; 55 = 5 × 11.
⇒ Since 5 is the only common prime factor of 210 and 55. Hence, HCF (210, 55) = 5.
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