Highest Common Factor of 680, 376 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 680, 376 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 376 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 680, 376 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 680, 376 is 8.
HCF(680, 376) = 8
HCF of 680, 376 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 376 is 8.
Highest Common Factor of 680,376 is 8
Step 1: Since 680 > 376, we apply the division lemma to 680 and 376, to get
680 = 376 x 1 + 304
Step 2: Since the reminder 376 ≠ 0, we apply division lemma to 304 and 376, to get
376 = 304 x 1 + 72
Step 3: We consider the new divisor 304 and the new remainder 72, and apply the division lemma to get
304 = 72 x 4 + 16
We consider the new divisor 72 and the new remainder 16,and apply the division lemma to get
72 = 16 x 4 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 680 and 376 is 8
Notice that 8 = HCF(16,8) = HCF(72,16) = HCF(304,72) = HCF(376,304) = HCF(680,376) .
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Frequently Asked Questions on HCF of 680, 376 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 680, 376?
Answer: HCF of 680, 376 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 376 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 376 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.