Highest Common Factor of 377, 638, 198 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 377, 638, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 377, 638, 198 is 1 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 377, 638, 198 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 377, 638, 198 is 1.
HCF(377, 638, 198) = 1
HCF of 377, 638, 198 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 377, 638, 198 is 1.
Highest Common Factor of 377,638,198 is 1
Step 1: Since 638 > 377, we apply the division lemma to 638 and 377, to get
638 = 377 x 1 + 261
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 261 and 377, to get
377 = 261 x 1 + 116
Step 3: We consider the new divisor 261 and the new remainder 116, and apply the division lemma to get
261 = 116 x 2 + 29
We consider the new divisor 116 and the new remainder 29, and apply the division lemma to get
116 = 29 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 377 and 638 is 29
Notice that 29 = HCF(116,29) = HCF(261,116) = HCF(377,261) = HCF(638,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 198 > 29, we apply the division lemma to 198 and 29, to get
198 = 29 x 6 + 24
Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 24 and 29, to get
29 = 24 x 1 + 5
Step 3: We consider the new divisor 24 and the new remainder 5, and apply the division lemma to get
24 = 5 x 4 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 198 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(198,29) .
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Frequently Asked Questions on HCF of 377, 638, 198 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 377, 638, 198?
Answer: HCF of 377, 638, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 377, 638, 198 using Euclid's Algorithm?
Answer: For arbitrary numbers 377, 638, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
