Highest Common Factor of 410, 770, 854 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 410, 770, 854 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 770, 854 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 410, 770, 854 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 410, 770, 854 is 2.
HCF(410, 770, 854) = 2
HCF of 410, 770, 854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 770, 854 is 2.
Highest Common Factor of 410,770,854 is 2
Step 1: Since 770 > 410, we apply the division lemma to 770 and 410, to get
770 = 410 x 1 + 360
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 360 and 410, to get
410 = 360 x 1 + 50
Step 3: We consider the new divisor 360 and the new remainder 50, and apply the division lemma to get
360 = 50 x 7 + 10
We consider the new divisor 50 and the new remainder 10, and apply the division lemma to get
50 = 10 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 410 and 770 is 10
Notice that 10 = HCF(50,10) = HCF(360,50) = HCF(410,360) = HCF(770,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 854 > 10, we apply the division lemma to 854 and 10, to get
854 = 10 x 85 + 4
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get
10 = 4 x 2 + 2
Step 3: 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 10 and 854 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(854,10) .
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Frequently Asked Questions on HCF of 410, 770, 854 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 410, 770, 854?
Answer: HCF of 410, 770, 854 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 770, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 770, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.