Highest Common Factor of 678, 304, 676 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 678, 304, 676 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 304, 676 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 678, 304, 676 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 678, 304, 676 is 2.
HCF(678, 304, 676) = 2
HCF of 678, 304, 676 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 304, 676 is 2.
Highest Common Factor of 678,304,676 is 2
Step 1: Since 678 > 304, we apply the division lemma to 678 and 304, to get
678 = 304 x 2 + 70
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 70 and 304, to get
304 = 70 x 4 + 24
Step 3: We consider the new divisor 70 and the new remainder 24, and apply the division lemma to get
70 = 24 x 2 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 304 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(70,24) = HCF(304,70) = HCF(678,304) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 676 > 2, we apply the division lemma to 676 and 2, to get
676 = 2 x 338 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 676 is 2
Notice that 2 = HCF(676,2) .
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Frequently Asked Questions on HCF of 678, 304, 676 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 678, 304, 676?
Answer: HCF of 678, 304, 676 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 304, 676 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 304, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.