Highest Common Factor of 843, 972, 859 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 843, 972, 859 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 843, 972, 859 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 843, 972, 859 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 843, 972, 859 is 1.
HCF(843, 972, 859) = 1
HCF of 843, 972, 859 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 843, 972, 859 is 1.
Highest Common Factor of 843,972,859 is 1
Step 1: Since 972 > 843, we apply the division lemma to 972 and 843, to get
972 = 843 x 1 + 129
Step 2: Since the reminder 843 ≠ 0, we apply division lemma to 129 and 843, to get
843 = 129 x 6 + 69
Step 3: We consider the new divisor 129 and the new remainder 69, and apply the division lemma to get
129 = 69 x 1 + 60
We consider the new divisor 69 and the new remainder 60,and apply the division lemma to get
69 = 60 x 1 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 843 and 972 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(69,60) = HCF(129,69) = HCF(843,129) = HCF(972,843) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 859 > 3, we apply the division lemma to 859 and 3, to get
859 = 3 x 286 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 859 is 1
Notice that 1 = HCF(3,1) = HCF(859,3) .
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Frequently Asked Questions on HCF of 843, 972, 859 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 843, 972, 859?
Answer: HCF of 843, 972, 859 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 843, 972, 859 using Euclid's Algorithm?
Answer: For arbitrary numbers 843, 972, 859 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.