Highest Common Factor of 584, 422, 140 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 584, 422, 140 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 422, 140 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 584, 422, 140 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 584, 422, 140 is 2.
HCF(584, 422, 140) = 2
HCF of 584, 422, 140 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 584, 422, 140 is 2.
Highest Common Factor of 584,422,140 is 2
Step 1: Since 584 > 422, we apply the division lemma to 584 and 422, to get
584 = 422 x 1 + 162
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 162 and 422, to get
422 = 162 x 2 + 98
Step 3: We consider the new divisor 162 and the new remainder 98, and apply the division lemma to get
162 = 98 x 1 + 64
We consider the new divisor 98 and the new remainder 64,and apply the division lemma to get
98 = 64 x 1 + 34
We consider the new divisor 64 and the new remainder 34,and apply the division lemma to get
64 = 34 x 1 + 30
We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
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 584 and 422 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(64,34) = HCF(98,64) = HCF(162,98) = HCF(422,162) = HCF(584,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 140 > 2, we apply the division lemma to 140 and 2, to get
140 = 2 x 70 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 140 is 2
Notice that 2 = HCF(140,2) .
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Frequently Asked Questions on HCF of 584, 422, 140 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 584, 422, 140?
Answer: HCF of 584, 422, 140 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 422, 140 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 422, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.