Highest Common Factor of 6700, 7134 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 6700, 7134 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6700, 7134 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 6700, 7134 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 6700, 7134 is 2.
HCF(6700, 7134) = 2
HCF of 6700, 7134 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6700, 7134 is 2.
Highest Common Factor of 6700,7134 is 2
Step 1: Since 7134 > 6700, we apply the division lemma to 7134 and 6700, to get
7134 = 6700 x 1 + 434
Step 2: Since the reminder 6700 ≠ 0, we apply division lemma to 434 and 6700, to get
6700 = 434 x 15 + 190
Step 3: We consider the new divisor 434 and the new remainder 190, and apply the division lemma to get
434 = 190 x 2 + 54
We consider the new divisor 190 and the new remainder 54,and apply the division lemma to get
190 = 54 x 3 + 28
We consider the new divisor 54 and the new remainder 28,and apply the division lemma to get
54 = 28 x 1 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6700 and 7134 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(54,28) = HCF(190,54) = HCF(434,190) = HCF(6700,434) = HCF(7134,6700) .
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Frequently Asked Questions on HCF of 6700, 7134 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 6700, 7134?
Answer: HCF of 6700, 7134 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6700, 7134 using Euclid's Algorithm?
Answer: For arbitrary numbers 6700, 7134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.