Highest Common Factor of 820, 716, 663 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 820, 716, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 716, 663 is 1 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 820, 716, 663 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 820, 716, 663 is 1.
HCF(820, 716, 663) = 1
HCF of 820, 716, 663 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 716, 663 is 1.
Highest Common Factor of 820,716,663 is 1
Step 1: Since 820 > 716, we apply the division lemma to 820 and 716, to get
820 = 716 x 1 + 104
Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 104 and 716, to get
716 = 104 x 6 + 92
Step 3: We consider the new divisor 104 and the new remainder 92, and apply the division lemma to get
104 = 92 x 1 + 12
We consider the new divisor 92 and the new remainder 12,and apply the division lemma to get
92 = 12 x 7 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 820 and 716 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(92,12) = HCF(104,92) = HCF(716,104) = HCF(820,716) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 663 > 4, we apply the division lemma to 663 and 4, to get
663 = 4 x 165 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 663 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(663,4) .
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Frequently Asked Questions on HCF of 820, 716, 663 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 820, 716, 663?
Answer: HCF of 820, 716, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 716, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 716, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.