Highest Common Factor of 712, 976, 651 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 712, 976, 651 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 976, 651 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 712, 976, 651 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 712, 976, 651 is 1.
HCF(712, 976, 651) = 1
HCF of 712, 976, 651 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 976, 651 is 1.
Highest Common Factor of 712,976,651 is 1
Step 1: Since 976 > 712, we apply the division lemma to 976 and 712, to get
976 = 712 x 1 + 264
Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 264 and 712, to get
712 = 264 x 2 + 184
Step 3: We consider the new divisor 264 and the new remainder 184, and apply the division lemma to get
264 = 184 x 1 + 80
We consider the new divisor 184 and the new remainder 80,and apply the division lemma to get
184 = 80 x 2 + 24
We consider the new divisor 80 and the new remainder 24,and apply the division lemma to get
80 = 24 x 3 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 976 is 8
Notice that 8 = HCF(24,8) = HCF(80,24) = HCF(184,80) = HCF(264,184) = HCF(712,264) = HCF(976,712) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 651 > 8, we apply the division lemma to 651 and 8, to get
651 = 8 x 81 + 3
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 3 and 8, to get
8 = 3 x 2 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 8 and 651 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(651,8) .
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Frequently Asked Questions on HCF of 712, 976, 651 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 712, 976, 651?
Answer: HCF of 712, 976, 651 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 976, 651 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 976, 651 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.