Highest Common Factor of 6680, 344 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 6680, 344 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 6680, 344 is 8 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 6680, 344 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 6680, 344 is 8.
HCF(6680, 344) = 8
HCF of 6680, 344 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6680, 344 is 8.
Highest Common Factor of 6680,344 is 8
Step 1: Since 6680 > 344, we apply the division lemma to 6680 and 344, to get
6680 = 344 x 19 + 144
Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 144 and 344, to get
344 = 144 x 2 + 56
Step 3: We consider the new divisor 144 and the new remainder 56, and apply the division lemma to get
144 = 56 x 2 + 32
We consider the new divisor 56 and the new remainder 32,and apply the division lemma to get
56 = 32 x 1 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 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 6680 and 344 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(56,32) = HCF(144,56) = HCF(344,144) = HCF(6680,344) .
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Frequently Asked Questions on HCF of 6680, 344 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 6680, 344?
Answer: HCF of 6680, 344 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6680, 344 using Euclid's Algorithm?
Answer: For arbitrary numbers 6680, 344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.