Highest Common Factor of 992, 564, 322 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 992, 564, 322 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 992, 564, 322 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 992, 564, 322 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 992, 564, 322 is 2.
HCF(992, 564, 322) = 2
HCF of 992, 564, 322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 992, 564, 322 is 2.
Highest Common Factor of 992,564,322 is 2
Step 1: Since 992 > 564, we apply the division lemma to 992 and 564, to get
992 = 564 x 1 + 428
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 428 and 564, to get
564 = 428 x 1 + 136
Step 3: We consider the new divisor 428 and the new remainder 136, and apply the division lemma to get
428 = 136 x 3 + 20
We consider the new divisor 136 and the new remainder 20,and apply the division lemma to get
136 = 20 x 6 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 992 and 564 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(136,20) = HCF(428,136) = HCF(564,428) = HCF(992,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 322 > 4, we apply the division lemma to 322 and 4, to get
322 = 4 x 80 + 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 322 is 2
Notice that 2 = HCF(4,2) = HCF(322,4) .
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Frequently Asked Questions on HCF of 992, 564, 322 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 992, 564, 322?
Answer: HCF of 992, 564, 322 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 992, 564, 322 using Euclid's Algorithm?
Answer: For arbitrary numbers 992, 564, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.