Highest Common Factor of 88, 212, 286 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 88, 212, 286 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 88, 212, 286 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 88, 212, 286 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 88, 212, 286 is 2.
HCF(88, 212, 286) = 2
HCF of 88, 212, 286 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 88, 212, 286 is 2.
Highest Common Factor of 88,212,286 is 2
Step 1: Since 212 > 88, we apply the division lemma to 212 and 88, to get
212 = 88 x 2 + 36
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 36 and 88, to get
88 = 36 x 2 + 16
Step 3: We consider the new divisor 36 and the new remainder 16, and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 88 and 212 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(88,36) = HCF(212,88) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 286 > 4, we apply the division lemma to 286 and 4, to get
286 = 4 x 71 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 286 is 2
Notice that 2 = HCF(4,2) = HCF(286,4) .
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Frequently Asked Questions on HCF of 88, 212, 286 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 88, 212, 286?
Answer: HCF of 88, 212, 286 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 88, 212, 286 using Euclid's Algorithm?
Answer: For arbitrary numbers 88, 212, 286 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.