Highest Common Factor of 714, 561, 838 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 714, 561, 838 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 561, 838 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 714, 561, 838 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 714, 561, 838 is 1.
HCF(714, 561, 838) = 1
HCF of 714, 561, 838 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 561, 838 is 1.
Highest Common Factor of 714,561,838 is 1
Step 1: Since 714 > 561, we apply the division lemma to 714 and 561, to get
714 = 561 x 1 + 153
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 153 and 561, to get
561 = 153 x 3 + 102
Step 3: We consider the new divisor 153 and the new remainder 102, and apply the division lemma to get
153 = 102 x 1 + 51
We consider the new divisor 102 and the new remainder 51, and apply the division lemma to get
102 = 51 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 714 and 561 is 51
Notice that 51 = HCF(102,51) = HCF(153,102) = HCF(561,153) = HCF(714,561) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 838 > 51, we apply the division lemma to 838 and 51, to get
838 = 51 x 16 + 22
Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 22 and 51, to get
51 = 22 x 2 + 7
Step 3: We consider the new divisor 22 and the new remainder 7, and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 51 and 838 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(51,22) = HCF(838,51) .
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Frequently Asked Questions on HCF of 714, 561, 838 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 714, 561, 838?
Answer: HCF of 714, 561, 838 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 561, 838 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 561, 838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.