Highest Common Factor of 198, 234, 380, 382 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 198, 234, 380, 382 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 234, 380, 382 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 198, 234, 380, 382 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 198, 234, 380, 382 is 2.
HCF(198, 234, 380, 382) = 2
HCF of 198, 234, 380, 382 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 234, 380, 382 is 2.
Highest Common Factor of 198,234,380,382 is 2
Step 1: Since 234 > 198, we apply the division lemma to 234 and 198, to get
234 = 198 x 1 + 36
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 36 and 198, to get
198 = 36 x 5 + 18
Step 3: We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 198 and 234 is 18
Notice that 18 = HCF(36,18) = HCF(198,36) = HCF(234,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 380 > 18, we apply the division lemma to 380 and 18, to get
380 = 18 x 21 + 2
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 2 and 18, to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 380 is 2
Notice that 2 = HCF(18,2) = HCF(380,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 382 > 2, we apply the division lemma to 382 and 2, to get
382 = 2 x 191 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 382 is 2
Notice that 2 = HCF(382,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 198, 234, 380, 382 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 198, 234, 380, 382?
Answer: HCF of 198, 234, 380, 382 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 234, 380, 382 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 234, 380, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.