Highest Common Factor of 367, 6740 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 367, 6740 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 367, 6740 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 367, 6740 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 367, 6740 is 1.
HCF(367, 6740) = 1
HCF of 367, 6740 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 367, 6740 is 1.
Highest Common Factor of 367,6740 is 1
Step 1: Since 6740 > 367, we apply the division lemma to 6740 and 367, to get
6740 = 367 x 18 + 134
Step 2: Since the reminder 367 ≠ 0, we apply division lemma to 134 and 367, to get
367 = 134 x 2 + 99
Step 3: We consider the new divisor 134 and the new remainder 99, and apply the division lemma to get
134 = 99 x 1 + 35
We consider the new divisor 99 and the new remainder 35,and apply the division lemma to get
99 = 35 x 2 + 29
We consider the new divisor 35 and the new remainder 29,and apply the division lemma to get
35 = 29 x 1 + 6
We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get
29 = 6 x 4 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 367 and 6740 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(35,29) = HCF(99,35) = HCF(134,99) = HCF(367,134) = HCF(6740,367) .
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Frequently Asked Questions on HCF of 367, 6740 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 367, 6740?
Answer: HCF of 367, 6740 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 367, 6740 using Euclid's Algorithm?
Answer: For arbitrary numbers 367, 6740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.