Highest Common Factor of 340, 940, 822 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 340, 940, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 940, 822 is 2 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 340, 940, 822 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 340, 940, 822 is 2.
HCF(340, 940, 822) = 2
HCF of 340, 940, 822 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 940, 822 is 2.
Highest Common Factor of 340,940,822 is 2
Step 1: Since 940 > 340, we apply the division lemma to 940 and 340, to get
940 = 340 x 2 + 260
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 260 and 340, to get
340 = 260 x 1 + 80
Step 3: We consider the new divisor 260 and the new remainder 80, and apply the division lemma to get
260 = 80 x 3 + 20
We consider the new divisor 80 and the new remainder 20, and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 340 and 940 is 20
Notice that 20 = HCF(80,20) = HCF(260,80) = HCF(340,260) = HCF(940,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 20, we apply the division lemma to 822 and 20, to get
822 = 20 x 41 + 2
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 2 and 20, to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 822 is 2
Notice that 2 = HCF(20,2) = HCF(822,20) .
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Frequently Asked Questions on HCF of 340, 940, 822 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 340, 940, 822?
Answer: HCF of 340, 940, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 940, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 940, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.