Highest Common Factor of 561, 884 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 561, 884 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 884 is 17 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 561, 884 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 561, 884 is 17.
HCF(561, 884) = 17
HCF of 561, 884 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 884 is 17.
Highest Common Factor of 561,884 is 17
Step 1: Since 884 > 561, we apply the division lemma to 884 and 561, to get
884 = 561 x 1 + 323
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 323 and 561, to get
561 = 323 x 1 + 238
Step 3: We consider the new divisor 323 and the new remainder 238, and apply the division lemma to get
323 = 238 x 1 + 85
We consider the new divisor 238 and the new remainder 85,and apply the division lemma to get
238 = 85 x 2 + 68
We consider the new divisor 85 and the new remainder 68,and apply the division lemma to get
85 = 68 x 1 + 17
We consider the new divisor 68 and the new remainder 17,and apply the division lemma to get
68 = 17 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 561 and 884 is 17
Notice that 17 = HCF(68,17) = HCF(85,68) = HCF(238,85) = HCF(323,238) = HCF(561,323) = HCF(884,561) .
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Frequently Asked Questions on HCF of 561, 884 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 561, 884?
Answer: HCF of 561, 884 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 884 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.