Highest Common Factor of 708, 9722, 8832 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 708, 9722, 8832 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 9722, 8832 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 708, 9722, 8832 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 708, 9722, 8832 is 2.
HCF(708, 9722, 8832) = 2
HCF of 708, 9722, 8832 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 9722, 8832 is 2.
Highest Common Factor of 708,9722,8832 is 2
Step 1: Since 9722 > 708, we apply the division lemma to 9722 and 708, to get
9722 = 708 x 13 + 518
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 518 and 708, to get
708 = 518 x 1 + 190
Step 3: We consider the new divisor 518 and the new remainder 190, and apply the division lemma to get
518 = 190 x 2 + 138
We consider the new divisor 190 and the new remainder 138,and apply the division lemma to get
190 = 138 x 1 + 52
We consider the new divisor 138 and the new remainder 52,and apply the division lemma to get
138 = 52 x 2 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 708 and 9722 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(138,52) = HCF(190,138) = HCF(518,190) = HCF(708,518) = HCF(9722,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8832 > 2, we apply the division lemma to 8832 and 2, to get
8832 = 2 x 4416 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8832 is 2
Notice that 2 = HCF(8832,2) .
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Frequently Asked Questions on HCF of 708, 9722, 8832 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 708, 9722, 8832?
Answer: HCF of 708, 9722, 8832 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 9722, 8832 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 9722, 8832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.