### HCF of 196 and 38220

**HCF of 196 and 38220: **HCF (Highest Common Factor or the Greatest common divisor) is any factor that divides the numbers equally. The number that divides both 196 and 38220 is 196. The methods to find HCF are:

- Listing Factor Method
- Long Division Method
- Prime Factorization Method.

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## HCF of 196 And 38220 Using the Listing Factor Method

Steps to find the HCF of the number using the listing factor method are given below:

Step 1: Find the factor for the given number.

Step 2: List the common factors

Step 3: The highest common factor is the HCF of the given number.

Therefore, the HCF of 196 and 38220 using the listing factor method.

Step 1: Find the factor for the given number.

The factor of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196

The factor 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

Step 2: List the common factors

There are about 9 common factors.

The common factors = 1, 2,4, 7, 14, 28, 49 98, 196.

Step 2: The highest common factor is the HCF of the given number.

The highest common factor = 196.

Hence, **HCF (196, 38220) = 196.**

## HCF of 196 and 38220 Using the Long Division Method

The long division method is one of the easiest and fastest ways to obtain the HCF of any number. The steps are as follows.

Step 1: Divide the larger number by the smaller number.

Step 2: The last divisor is the HCF of the given number.

Therefore, the HCF of 196 and 38220 using the long division method.

Step 1: Divide the larger number by the smaller number.

Step 2: The last divisor is the HCF of the given number.

The last divisor of 196 and 38220 is 196

Hence **HCF (196,38220) = 196**.

## HCF of 196 and 38220 Using the Prime Factorization Method

The following step is taken in order to find the HCF using the prime factorization method.

Step 1: Find the prime factors of the given numbers

Step 2: List the common prime numbers

Step 3: Multiply the common factors that are the HCF of the given number.

Therefore, the HCF of 196 and 38220 using the prime factorization method

Step 1: Find the prime factors of the given numbers

The prime factors of 196 = 2 × 2 × 7 × 7

The prime factors of 38220 = 2 × 2 × 3 × 5 × 7 × 7 × 13

Step 2: List the common prime numbers

The common prime numbers are = 2×2×7×7

Step 3: Multiply the common factors that are the HCF of the given number

Now multiply the common prime numbers 2×2×7×7 = 196

Hence, HCF **(196,38220) = 196**.

**Solved Examples:**

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

Given:

HCF (x, 196) = 196

LCM(x,196) = 38220

Therefore, LCM×HCF = 196 × (X)

X = (LCM × HCF) ∕ 196

Hence,

X = (196 × 38220) ∕ 196

Therefore, X = 38220 is the other number.

**Example 2: Find the HCF of 196 and 38220 using the prime factorization method **

The prime factors of 196 = 2 × 2 × 7 × 7

The prime factors of 38220 = 2 × 2 × 3 × 5 × 7 × 7 × 13

Hence HCF (196,38220) = 196.

**Example 3: The product of the two numbers is 7491120. If their HCF is 196, what is their LCM?**

LCM×HCF = product of two numbers

LCM = product of two numbers ∕ HCF

LCM = 30375 ∕ 196

Hence LCM = 38220.

**Example 4: Find the HCF of 135 and 225 using the division method. **

The HCF(135,225) = 45.

**Example 5: what is the HCF of 196 and 38220**

The factor of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196

The factor 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

The HCF(196,38220) = 196.

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**Frequently Asked Questions (FAQ):**

**What is the HCF of 196, 38220?**

The HCF(196,38220) = 196.

**What is the LCM of 196 and 38220 if their HCF is 196?**

The LCM of (196,38220) = 38220

**What is the product of 196 and 38220?**

The product of 196 and 38220 = 7491120

**What is the common factors in 196 and 38220?**

The common factors of 196 and 38220 = 1, 2,4, 7, 14, 28, 49 98, 196.

**Find the greatest common divisor for 196 and 38220.**

The GCD (196,38220) = 196.

**What is the number that can divide 196 and 38220 completely?**

The number that can divide by 196 and 38220 = 196.

Written by

Prerit Jain