Highest Common Factor of 662, 923, 706 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 662, 923, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 923, 706 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 662, 923, 706 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 662, 923, 706 is 1.
HCF(662, 923, 706) = 1
HCF of 662, 923, 706 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 923, 706 is 1.
Highest Common Factor of 662,923,706 is 1
Step 1: Since 923 > 662, we apply the division lemma to 923 and 662, to get
923 = 662 x 1 + 261
Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 261 and 662, to get
662 = 261 x 2 + 140
Step 3: We consider the new divisor 261 and the new remainder 140, and apply the division lemma to get
261 = 140 x 1 + 121
We consider the new divisor 140 and the new remainder 121,and apply the division lemma to get
140 = 121 x 1 + 19
We consider the new divisor 121 and the new remainder 19,and apply the division lemma to get
121 = 19 x 6 + 7
We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get
19 = 7 x 2 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 662 and 923 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(121,19) = HCF(140,121) = HCF(261,140) = HCF(662,261) = HCF(923,662) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 706 > 1, we apply the division lemma to 706 and 1, to get
706 = 1 x 706 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 706 is 1
Notice that 1 = HCF(706,1) .
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Frequently Asked Questions on HCF of 662, 923, 706 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 662, 923, 706?
Answer: HCF of 662, 923, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 923, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 923, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.