Highest Common Factor of 198, 316, 651 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, 316, 651 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 316, 651 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 198, 316, 651 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, 316, 651 is 1.
HCF(198, 316, 651) = 1
HCF of 198, 316, 651 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, 316, 651 is 1.
Highest Common Factor of 198,316,651 is 1
Step 1: Since 316 > 198, we apply the division lemma to 316 and 198, to get
316 = 198 x 1 + 118
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 118 and 198, to get
198 = 118 x 1 + 80
Step 3: We consider the new divisor 118 and the new remainder 80, and apply the division lemma to get
118 = 80 x 1 + 38
We consider the new divisor 80 and the new remainder 38,and apply the division lemma to get
80 = 38 x 2 + 4
We consider the new divisor 38 and the new remainder 4,and apply the division lemma to get
38 = 4 x 9 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 198 and 316 is 2
Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(80,38) = HCF(118,80) = HCF(198,118) = HCF(316,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 651 > 2, we apply the division lemma to 651 and 2, to get
651 = 2 x 325 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 651 is 1
Notice that 1 = HCF(2,1) = HCF(651,2) .
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Frequently Asked Questions on HCF of 198, 316, 651 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, 316, 651?
Answer: HCF of 198, 316, 651 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 316, 651 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 316, 651 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.