Highest Common Factor of 509, 870, 920 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 509, 870, 920 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 870, 920 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 509, 870, 920 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 509, 870, 920 is 1.
HCF(509, 870, 920) = 1
HCF of 509, 870, 920 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 509, 870, 920 is 1.
Highest Common Factor of 509,870,920 is 1
Step 1: Since 870 > 509, we apply the division lemma to 870 and 509, to get
870 = 509 x 1 + 361
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 361 and 509, to get
509 = 361 x 1 + 148
Step 3: We consider the new divisor 361 and the new remainder 148, and apply the division lemma to get
361 = 148 x 2 + 65
We consider the new divisor 148 and the new remainder 65,and apply the division lemma to get
148 = 65 x 2 + 18
We consider the new divisor 65 and the new remainder 18,and apply the division lemma to get
65 = 18 x 3 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 870 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(65,18) = HCF(148,65) = HCF(361,148) = HCF(509,361) = HCF(870,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 920 > 1, we apply the division lemma to 920 and 1, to get
920 = 1 x 920 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 920 is 1
Notice that 1 = HCF(920,1) .
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Frequently Asked Questions on HCF of 509, 870, 920 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 509, 870, 920?
Answer: HCF of 509, 870, 920 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 870, 920 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 870, 920 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.