Highest Common Factor of 584, 900, 922 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, 900, 922 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 900, 922 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, 900, 922 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, 900, 922 is 2.
HCF(584, 900, 922) = 2
HCF of 584, 900, 922 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, 900, 922 is 2.
Highest Common Factor of 584,900,922 is 2
Step 1: Since 900 > 584, we apply the division lemma to 900 and 584, to get
900 = 584 x 1 + 316
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 316 and 584, to get
584 = 316 x 1 + 268
Step 3: We consider the new divisor 316 and the new remainder 268, and apply the division lemma to get
316 = 268 x 1 + 48
We consider the new divisor 268 and the new remainder 48,and apply the division lemma to get
268 = 48 x 5 + 28
We consider the new divisor 48 and the new remainder 28,and apply the division lemma to get
48 = 28 x 1 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 584 and 900 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(268,48) = HCF(316,268) = HCF(584,316) = HCF(900,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 922 > 4, we apply the division lemma to 922 and 4, to get
922 = 4 x 230 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 922 is 2
Notice that 2 = HCF(4,2) = HCF(922,4) .
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Frequently Asked Questions on HCF of 584, 900, 922 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, 900, 922?
Answer: HCF of 584, 900, 922 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 900, 922 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 900, 922 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.