Highest Common Factor of 894, 610, 684 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 894, 610, 684 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 894, 610, 684 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 894, 610, 684 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 894, 610, 684 is 2.
HCF(894, 610, 684) = 2
HCF of 894, 610, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 894, 610, 684 is 2.
Highest Common Factor of 894,610,684 is 2
Step 1: Since 894 > 610, we apply the division lemma to 894 and 610, to get
894 = 610 x 1 + 284
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 284 and 610, to get
610 = 284 x 2 + 42
Step 3: We consider the new divisor 284 and the new remainder 42, and apply the division lemma to get
284 = 42 x 6 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 894 and 610 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(284,42) = HCF(610,284) = HCF(894,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 2, we apply the division lemma to 684 and 2, to get
684 = 2 x 342 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 684 is 2
Notice that 2 = HCF(684,2) .
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Frequently Asked Questions on HCF of 894, 610, 684 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 894, 610, 684?
Answer: HCF of 894, 610, 684 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 894, 610, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 894, 610, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.