Highest Common Factor of 108, 111, 662 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 108, 111, 662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 108, 111, 662 is 1 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 108, 111, 662 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 108, 111, 662 is 1.
HCF(108, 111, 662) = 1
HCF of 108, 111, 662 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 108, 111, 662 is 1.
Highest Common Factor of 108,111,662 is 1
Step 1: Since 111 > 108, we apply the division lemma to 111 and 108, to get
111 = 108 x 1 + 3
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 3 and 108, to get
108 = 3 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 108 and 111 is 3
Notice that 3 = HCF(108,3) = HCF(111,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 662 > 3, we apply the division lemma to 662 and 3, to get
662 = 3 x 220 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 662 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(662,3) .
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Frequently Asked Questions on HCF of 108, 111, 662 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 108, 111, 662?
Answer: HCF of 108, 111, 662 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 108, 111, 662 using Euclid's Algorithm?
Answer: For arbitrary numbers 108, 111, 662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.