Highest Common Factor of 667, 746, 765 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 667, 746, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 746, 765 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 667, 746, 765 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 667, 746, 765 is 1.
HCF(667, 746, 765) = 1
HCF of 667, 746, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 746, 765 is 1.
Highest Common Factor of 667,746,765 is 1
Step 1: Since 746 > 667, we apply the division lemma to 746 and 667, to get
746 = 667 x 1 + 79
Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 79 and 667, to get
667 = 79 x 8 + 35
Step 3: We consider the new divisor 79 and the new remainder 35, and apply the division lemma to get
79 = 35 x 2 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 746 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(79,35) = HCF(667,79) = HCF(746,667) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 1, we apply the division lemma to 765 and 1, to get
765 = 1 x 765 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 765 is 1
Notice that 1 = HCF(765,1) .
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Frequently Asked Questions on HCF of 667, 746, 765 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 667, 746, 765?
Answer: HCF of 667, 746, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 746, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 746, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.