Highest Common Factor of 917, 666, 735 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 917, 666, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 917, 666, 735 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 917, 666, 735 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 917, 666, 735 is 1.
HCF(917, 666, 735) = 1
HCF of 917, 666, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 917, 666, 735 is 1.
Highest Common Factor of 917,666,735 is 1
Step 1: Since 917 > 666, we apply the division lemma to 917 and 666, to get
917 = 666 x 1 + 251
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 251 and 666, to get
666 = 251 x 2 + 164
Step 3: We consider the new divisor 251 and the new remainder 164, and apply the division lemma to get
251 = 164 x 1 + 87
We consider the new divisor 164 and the new remainder 87,and apply the division lemma to get
164 = 87 x 1 + 77
We consider the new divisor 87 and the new remainder 77,and apply the division lemma to get
87 = 77 x 1 + 10
We consider the new divisor 77 and the new remainder 10,and apply the division lemma to get
77 = 10 x 7 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
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 917 and 666 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(77,10) = HCF(87,77) = HCF(164,87) = HCF(251,164) = HCF(666,251) = HCF(917,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get
735 = 1 x 735 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1
Notice that 1 = HCF(735,1) .
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Frequently Asked Questions on HCF of 917, 666, 735 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 917, 666, 735?
Answer: HCF of 917, 666, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 917, 666, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 917, 666, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.