Highest Common Factor of 279, 492, 689 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 279, 492, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 279, 492, 689 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 279, 492, 689 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 279, 492, 689 is 1.
HCF(279, 492, 689) = 1
HCF of 279, 492, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 279, 492, 689 is 1.
Highest Common Factor of 279,492,689 is 1
Step 1: Since 492 > 279, we apply the division lemma to 492 and 279, to get
492 = 279 x 1 + 213
Step 2: Since the reminder 279 ≠ 0, we apply division lemma to 213 and 279, to get
279 = 213 x 1 + 66
Step 3: We consider the new divisor 213 and the new remainder 66, and apply the division lemma to get
213 = 66 x 3 + 15
We consider the new divisor 66 and the new remainder 15,and apply the division lemma to get
66 = 15 x 4 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 279 and 492 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(66,15) = HCF(213,66) = HCF(279,213) = HCF(492,279) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 689 > 3, we apply the division lemma to 689 and 3, to get
689 = 3 x 229 + 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 689 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(689,3) .
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Frequently Asked Questions on HCF of 279, 492, 689 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 279, 492, 689?
Answer: HCF of 279, 492, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 279, 492, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 279, 492, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
