Highest Common Factor of 708, 6114 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 708, 6114 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 6114 is 6 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 708, 6114 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 708, 6114 is 6.
HCF(708, 6114) = 6
HCF of 708, 6114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 6114 is 6.
Highest Common Factor of 708,6114 is 6
Step 1: Since 6114 > 708, we apply the division lemma to 6114 and 708, to get
6114 = 708 x 8 + 450
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 450 and 708, to get
708 = 450 x 1 + 258
Step 3: We consider the new divisor 450 and the new remainder 258, and apply the division lemma to get
450 = 258 x 1 + 192
We consider the new divisor 258 and the new remainder 192,and apply the division lemma to get
258 = 192 x 1 + 66
We consider the new divisor 192 and the new remainder 66,and apply the division lemma to get
192 = 66 x 2 + 60
We consider the new divisor 66 and the new remainder 60,and apply the division lemma to get
66 = 60 x 1 + 6
We consider the new divisor 60 and the new remainder 6,and apply the division lemma to get
60 = 6 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 708 and 6114 is 6
Notice that 6 = HCF(60,6) = HCF(66,60) = HCF(192,66) = HCF(258,192) = HCF(450,258) = HCF(708,450) = HCF(6114,708) .
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Frequently Asked Questions on HCF of 708, 6114 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 708, 6114?
Answer: HCF of 708, 6114 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 6114 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 6114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.