Highest Common Factor of 630, 806, 766 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 630, 806, 766 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 806, 766 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 630, 806, 766 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 630, 806, 766 is 2.
HCF(630, 806, 766) = 2
HCF of 630, 806, 766 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 630, 806, 766 is 2.
Highest Common Factor of 630,806,766 is 2
Step 1: Since 806 > 630, we apply the division lemma to 806 and 630, to get
806 = 630 x 1 + 176
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 176 and 630, to get
630 = 176 x 3 + 102
Step 3: We consider the new divisor 176 and the new remainder 102, and apply the division lemma to get
176 = 102 x 1 + 74
We consider the new divisor 102 and the new remainder 74,and apply the division lemma to get
102 = 74 x 1 + 28
We consider the new divisor 74 and the new remainder 28,and apply the division lemma to get
74 = 28 x 2 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 630 and 806 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(74,28) = HCF(102,74) = HCF(176,102) = HCF(630,176) = HCF(806,630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 766 > 2, we apply the division lemma to 766 and 2, to get
766 = 2 x 383 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 766 is 2
Notice that 2 = HCF(766,2) .
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Frequently Asked Questions on HCF of 630, 806, 766 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 630, 806, 766?
Answer: HCF of 630, 806, 766 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 806, 766 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 806, 766 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.