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HCF of 196 and 38220

HCF of 196 and 38220 is the largest possible number that divides 196 and 38220 exactly without any remainder. The factors of 196 and 38220 are 1, 2, 4, 7, 14, 28, 49, 98, 196 and 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110, 38220 respectively. There are 3 commonly used methods to find the HCF of 196 and 38220 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 196 and 38220
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 196 and 38220?

Answer: HCF of 196 and 38220 is 196.

Explanation:

The HCF of two non-zero integers, x(196) and y(38220), is the highest positive integer m(196) that divides both x(196) and y(38220) without any remainder.

Methods to Find HCF of 196 and 38220

Let's look at the different methods for finding the HCF of 196 and 38220.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 196 and 38220 by Prime Factorization

Prime factorization of 196 and 38220 is (2 × 2 × 7 × 7) and (2 × 2 × 3 × 5 × 7 × 7 × 13) respectively. As visible, 196 and 38220 have common prime factors. Hence, the HCF of 196 and 38220 is 2 × 2 × 7 × 7 = 196.

HCF of 196 and 38220 by Long Division

HCF of 196 and 38220 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 38220 (larger number) by 196 (smaller number).
Step 2: Since the remainder = 0, the divisor (196) is the HCF of 196 and 38220.

The corresponding divisor (196) is the HCF of 196 and 38220.

HCF of 196 and 38220 by Listing Common Factors

Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196
Factors of 38220: 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110, 38220

There are 9 common factors of 196 and 38220, that are 1, 2, 98, 196, 4, 7, 14, 49, and 28. Therefore, the highest common factor of 196 and 38220 is 196.

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HCF of 196 and 38220 Examples

Example 1: For two numbers, HCF = 196 and LCM = 38220. If one number is 196, find the other number.

Solution:

Given: HCF (x, 196) = 196 and LCM (x, 196) = 38220
∵ HCF × LCM = 196 × (x)
⇒ x = (HCF × LCM)/196
⇒ x = (196 × 38220)/196
⇒ x = 38220
Therefore, the other number is 38220.
Example 2: Find the highest number that divides 196 and 38220 exactly.

Solution:

The highest number that divides 196 and 38220 exactly is their highest common factor, i.e. HCF of 196 and 38220.
⇒ Factors of 196 and 38220:
- Factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196
- Factors of 38220 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110, 38220
Therefore, the HCF of 196 and 38220 is 196.
Example 3: The product of two numbers is 7491120. If their HCF is 196, what is their LCM?

Solution:

Given: HCF = 196 and product of numbers = 7491120
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 7491120/196
Therefore, the LCM is 38220.

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FAQs on HCF of 196 and 38220

What is the HCF of 196 and 38220?

The HCF of 196 and 38220 is 196. To calculate the HCF of 196 and 38220, we need to factor each number (factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196; factors of 38220 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110, 38220) and choose the highest factor that exactly divides both 196 and 38220, i.e., 196.

How to Find the HCF of 196 and 38220 by Long Division Method?

To find the HCF of 196, 38220 using long division method, 38220 is divided by 196. The corresponding divisor (196) when remainder equals 0 is taken as HCF.

If the HCF of 38220 and 196 is 196, Find its LCM.

HCF(38220, 196) × LCM(38220, 196) = 38220 × 196
Since the HCF of 38220 and 196 = 196
⇒ 196 × LCM(38220, 196) = 7491120
Therefore, LCM = 38220
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What is the Relation Between LCM and HCF of 196, 38220?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 196 and 38220, i.e. HCF × LCM = 196 × 38220.

What are the Methods to Find HCF of 196 and 38220?

There are three commonly used methods to find the HCF of 196 and 38220.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the HCF of 196 and 38220 by Prime Factorization?

To find the HCF of 196 and 38220, we will find the prime factorization of the given numbers, i.e. 196 = 2 × 2 × 7 × 7; 38220 = 2 × 2 × 3 × 5 × 7 × 7 × 13.
⇒ Since 2, 2, 7, 7 are common terms in the prime factorization of 196 and 38220. Hence, HCF(196, 38220) = 2 × 2 × 7 × 7 = 196
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