Highest Common Factor of 591, 990, 870, 540 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 591, 990, 870, 540 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 591, 990, 870, 540 is 3 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 591, 990, 870, 540 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 591, 990, 870, 540 is 3.
HCF(591, 990, 870, 540) = 3
HCF of 591, 990, 870, 540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 591, 990, 870, 540 is 3.
Highest Common Factor of 591,990,870,540 is 3
Step 1: Since 990 > 591, we apply the division lemma to 990 and 591, to get
990 = 591 x 1 + 399
Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 399 and 591, to get
591 = 399 x 1 + 192
Step 3: We consider the new divisor 399 and the new remainder 192, and apply the division lemma to get
399 = 192 x 2 + 15
We consider the new divisor 192 and the new remainder 15,and apply the division lemma to get
192 = 15 x 12 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 591 and 990 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(192,15) = HCF(399,192) = HCF(591,399) = HCF(990,591) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 3, we apply the division lemma to 870 and 3, to get
870 = 3 x 290 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 870 is 3
Notice that 3 = HCF(870,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 540 > 3, we apply the division lemma to 540 and 3, to get
540 = 3 x 180 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 540 is 3
Notice that 3 = HCF(540,3) .
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Frequently Asked Questions on HCF of 591, 990, 870, 540 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 591, 990, 870, 540?
Answer: HCF of 591, 990, 870, 540 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 591, 990, 870, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 591, 990, 870, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.