Highest Common Factor of 838, 110, 708 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 838, 110, 708 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 838, 110, 708 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 838, 110, 708 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 838, 110, 708 is 2.
HCF(838, 110, 708) = 2
HCF of 838, 110, 708 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 838, 110, 708 is 2.
Highest Common Factor of 838,110,708 is 2
Step 1: Since 838 > 110, we apply the division lemma to 838 and 110, to get
838 = 110 x 7 + 68
Step 2: Since the reminder 110 ≠ 0, we apply division lemma to 68 and 110, to get
110 = 68 x 1 + 42
Step 3: We consider the new divisor 68 and the new remainder 42, and apply the division lemma to get
68 = 42 x 1 + 26
We consider the new divisor 42 and the new remainder 26,and apply the division lemma to get
42 = 26 x 1 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 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 838 and 110 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(68,42) = HCF(110,68) = HCF(838,110) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 708 > 2, we apply the division lemma to 708 and 2, to get
708 = 2 x 354 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 708 is 2
Notice that 2 = HCF(708,2) .
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Frequently Asked Questions on HCF of 838, 110, 708 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 838, 110, 708?
Answer: HCF of 838, 110, 708 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 838, 110, 708 using Euclid's Algorithm?
Answer: For arbitrary numbers 838, 110, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.