Highest Common Factor of 600, 991, 459 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 600, 991, 459 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 991, 459 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 600, 991, 459 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 600, 991, 459 is 1.
HCF(600, 991, 459) = 1
HCF of 600, 991, 459 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 600, 991, 459 is 1.
Highest Common Factor of 600,991,459 is 1
Step 1: Since 991 > 600, we apply the division lemma to 991 and 600, to get
991 = 600 x 1 + 391
Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 391 and 600, to get
600 = 391 x 1 + 209
Step 3: We consider the new divisor 391 and the new remainder 209, and apply the division lemma to get
391 = 209 x 1 + 182
We consider the new divisor 209 and the new remainder 182,and apply the division lemma to get
209 = 182 x 1 + 27
We consider the new divisor 182 and the new remainder 27,and apply the division lemma to get
182 = 27 x 6 + 20
We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get
27 = 20 x 1 + 7
We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 600 and 991 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(182,27) = HCF(209,182) = HCF(391,209) = HCF(600,391) = HCF(991,600) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 459 > 1, we apply the division lemma to 459 and 1, to get
459 = 1 x 459 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 459 is 1
Notice that 1 = HCF(459,1) .
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Frequently Asked Questions on HCF of 600, 991, 459 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 600, 991, 459?
Answer: HCF of 600, 991, 459 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 991, 459 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 991, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
