Highest Common Factor of 68, 642, 712 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 68, 642, 712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 68, 642, 712 is 2 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 68, 642, 712 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 68, 642, 712 is 2.
HCF(68, 642, 712) = 2
HCF of 68, 642, 712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 68, 642, 712 is 2.
Highest Common Factor of 68,642,712 is 2
Step 1: Since 642 > 68, we apply the division lemma to 642 and 68, to get
642 = 68 x 9 + 30
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 30 and 68, to get
68 = 30 x 2 + 8
Step 3: We consider the new divisor 30 and the new remainder 8, and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 68 and 642 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(68,30) = HCF(642,68) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 712 > 2, we apply the division lemma to 712 and 2, to get
712 = 2 x 356 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 712 is 2
Notice that 2 = HCF(712,2) .
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Frequently Asked Questions on HCF of 68, 642, 712 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 68, 642, 712?
Answer: HCF of 68, 642, 712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 68, 642, 712 using Euclid's Algorithm?
Answer: For arbitrary numbers 68, 642, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.