Highest Common Factor of 218, 992, 668 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 218, 992, 668 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 992, 668 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 218, 992, 668 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 218, 992, 668 is 2.
HCF(218, 992, 668) = 2
HCF of 218, 992, 668 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 218, 992, 668 is 2.
Highest Common Factor of 218,992,668 is 2
Step 1: Since 992 > 218, we apply the division lemma to 992 and 218, to get
992 = 218 x 4 + 120
Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 120 and 218, to get
218 = 120 x 1 + 98
Step 3: We consider the new divisor 120 and the new remainder 98, and apply the division lemma to get
120 = 98 x 1 + 22
We consider the new divisor 98 and the new remainder 22,and apply the division lemma to get
98 = 22 x 4 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 218 and 992 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(98,22) = HCF(120,98) = HCF(218,120) = HCF(992,218) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 668 > 2, we apply the division lemma to 668 and 2, to get
668 = 2 x 334 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 668 is 2
Notice that 2 = HCF(668,2) .
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Frequently Asked Questions on HCF of 218, 992, 668 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 218, 992, 668?
Answer: HCF of 218, 992, 668 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 992, 668 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 992, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.