Highest Common Factor of 688, 882, 680 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 688, 882, 680 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 882, 680 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 688, 882, 680 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 688, 882, 680 is 2.
HCF(688, 882, 680) = 2
HCF of 688, 882, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 882, 680 is 2.
Highest Common Factor of 688,882,680 is 2
Step 1: Since 882 > 688, we apply the division lemma to 882 and 688, to get
882 = 688 x 1 + 194
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 194 and 688, to get
688 = 194 x 3 + 106
Step 3: We consider the new divisor 194 and the new remainder 106, and apply the division lemma to get
194 = 106 x 1 + 88
We consider the new divisor 106 and the new remainder 88,and apply the division lemma to get
106 = 88 x 1 + 18
We consider the new divisor 88 and the new remainder 18,and apply the division lemma to get
88 = 18 x 4 + 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 688 and 882 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(88,18) = HCF(106,88) = HCF(194,106) = HCF(688,194) = HCF(882,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 2, we apply the division lemma to 680 and 2, to get
680 = 2 x 340 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 680 is 2
Notice that 2 = HCF(680,2) .
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Frequently Asked Questions on HCF of 688, 882, 680 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 688, 882, 680?
Answer: HCF of 688, 882, 680 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 882, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 882, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.