Highest Common Factor of 891, 340 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 891, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 891, 340 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 891, 340 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 891, 340 is 1.
HCF(891, 340) = 1
HCF of 891, 340 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 891, 340 is 1.
Highest Common Factor of 891,340 is 1
Step 1: Since 891 > 340, we apply the division lemma to 891 and 340, to get
891 = 340 x 2 + 211
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 211 and 340, to get
340 = 211 x 1 + 129
Step 3: We consider the new divisor 211 and the new remainder 129, and apply the division lemma to get
211 = 129 x 1 + 82
We consider the new divisor 129 and the new remainder 82,and apply the division lemma to get
129 = 82 x 1 + 47
We consider the new divisor 82 and the new remainder 47,and apply the division lemma to get
82 = 47 x 1 + 35
We consider the new divisor 47 and the new remainder 35,and apply the division lemma to get
47 = 35 x 1 + 12
We consider the new divisor 35 and the new remainder 12,and apply the division lemma to get
35 = 12 x 2 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 891 and 340 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(35,12) = HCF(47,35) = HCF(82,47) = HCF(129,82) = HCF(211,129) = HCF(340,211) = HCF(891,340) .
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Frequently Asked Questions on HCF of 891, 340 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 891, 340?
Answer: HCF of 891, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 891, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 891, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.