Highest Common Factor of 86, 68, 74, 118 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 86, 68, 74, 118 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 86, 68, 74, 118 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 86, 68, 74, 118 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 86, 68, 74, 118 is 2.
HCF(86, 68, 74, 118) = 2
HCF of 86, 68, 74, 118 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 86, 68, 74, 118 is 2.
Highest Common Factor of 86,68,74,118 is 2
Step 1: Since 86 > 68, we apply the division lemma to 86 and 68, to get
86 = 68 x 1 + 18
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 18 and 68, to get
68 = 18 x 3 + 14
Step 3: We consider the new divisor 18 and the new remainder 14, and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 86 and 68 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(68,18) = HCF(86,68) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 2, we apply the division lemma to 74 and 2, to get
74 = 2 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 74 is 2
Notice that 2 = HCF(74,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 2, we apply the division lemma to 118 and 2, to get
118 = 2 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 118 is 2
Notice that 2 = HCF(118,2) .
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Frequently Asked Questions on HCF of 86, 68, 74, 118 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 86, 68, 74, 118?
Answer: HCF of 86, 68, 74, 118 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 86, 68, 74, 118 using Euclid's Algorithm?
Answer: For arbitrary numbers 86, 68, 74, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.