Highest Common Factor of 766, 475, 734 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 766, 475, 734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 766, 475, 734 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 766, 475, 734 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 766, 475, 734 is 1.
HCF(766, 475, 734) = 1
HCF of 766, 475, 734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 766, 475, 734 is 1.
Highest Common Factor of 766,475,734 is 1
Step 1: Since 766 > 475, we apply the division lemma to 766 and 475, to get
766 = 475 x 1 + 291
Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 291 and 475, to get
475 = 291 x 1 + 184
Step 3: We consider the new divisor 291 and the new remainder 184, and apply the division lemma to get
291 = 184 x 1 + 107
We consider the new divisor 184 and the new remainder 107,and apply the division lemma to get
184 = 107 x 1 + 77
We consider the new divisor 107 and the new remainder 77,and apply the division lemma to get
107 = 77 x 1 + 30
We consider the new divisor 77 and the new remainder 30,and apply the division lemma to get
77 = 30 x 2 + 17
We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get
30 = 17 x 1 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 766 and 475 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(77,30) = HCF(107,77) = HCF(184,107) = HCF(291,184) = HCF(475,291) = HCF(766,475) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 734 > 1, we apply the division lemma to 734 and 1, to get
734 = 1 x 734 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 734 is 1
Notice that 1 = HCF(734,1) .
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Frequently Asked Questions on HCF of 766, 475, 734 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 766, 475, 734?
Answer: HCF of 766, 475, 734 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 766, 475, 734 using Euclid's Algorithm?
Answer: For arbitrary numbers 766, 475, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
