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HCF

HCF of 196 and 38220

Written by Prerit Jain

Updated on: 15 Feb 2023

HCF of 196 and 38220

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.

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.

Long Division Method

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. 

Long 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.

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

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