Highest Common Factor of 876, 310, 116 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 876, 310, 116 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 876, 310, 116 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 876, 310, 116 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 876, 310, 116 is 2.
HCF(876, 310, 116) = 2
HCF of 876, 310, 116 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 876, 310, 116 is 2.
Highest Common Factor of 876,310,116 is 2
Step 1: Since 876 > 310, we apply the division lemma to 876 and 310, to get
876 = 310 x 2 + 256
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 256 and 310, to get
310 = 256 x 1 + 54
Step 3: We consider the new divisor 256 and the new remainder 54, and apply the division lemma to get
256 = 54 x 4 + 40
We consider the new divisor 54 and the new remainder 40,and apply the division lemma to get
54 = 40 x 1 + 14
We consider the new divisor 40 and the new remainder 14,and apply the division lemma to get
40 = 14 x 2 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 876 and 310 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(54,40) = HCF(256,54) = HCF(310,256) = HCF(876,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 2, we apply the division lemma to 116 and 2, to get
116 = 2 x 58 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 116 is 2
Notice that 2 = HCF(116,2) .
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Frequently Asked Questions on HCF of 876, 310, 116 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 876, 310, 116?
Answer: HCF of 876, 310, 116 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 876, 310, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 876, 310, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.