Highest Common Factor of 760, 318, 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 760, 318, 676 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 760, 318, 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 760, 318, 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 760, 318, 676 is 2.
HCF(760, 318, 676) = 2
HCF of 760, 318, 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 760, 318, 676 is 2.
Highest Common Factor of 760,318,676 is 2
Step 1: Since 760 > 318, we apply the division lemma to 760 and 318, to get
760 = 318 x 2 + 124
Step 2: Since the reminder 318 ≠ 0, we apply division lemma to 124 and 318, to get
318 = 124 x 2 + 70
Step 3: We consider the new divisor 124 and the new remainder 70, and apply the division lemma to get
124 = 70 x 1 + 54
We consider the new divisor 70 and the new remainder 54,and apply the division lemma to get
70 = 54 x 1 + 16
We consider the new divisor 54 and the new remainder 16,and apply the division lemma to get
54 = 16 x 3 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 760 and 318 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(54,16) = HCF(70,54) = HCF(124,70) = HCF(318,124) = HCF(760,318) .
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 760, 318, 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 760, 318, 676?
Answer: HCF of 760, 318, 676 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 760, 318, 676 using Euclid's Algorithm?
Answer: For arbitrary numbers 760, 318, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.