Highest Common Factor of 985, 680, 605, 822 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 985, 680, 605, 822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 680, 605, 822 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 985, 680, 605, 822 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 985, 680, 605, 822 is 1.
HCF(985, 680, 605, 822) = 1
HCF of 985, 680, 605, 822 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 680, 605, 822 is 1.
Highest Common Factor of 985,680,605,822 is 1
Step 1: Since 985 > 680, we apply the division lemma to 985 and 680, to get
985 = 680 x 1 + 305
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 305 and 680, to get
680 = 305 x 2 + 70
Step 3: We consider the new divisor 305 and the new remainder 70, and apply the division lemma to get
305 = 70 x 4 + 25
We consider the new divisor 70 and the new remainder 25,and apply the division lemma to get
70 = 25 x 2 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 985 and 680 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(70,25) = HCF(305,70) = HCF(680,305) = HCF(985,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 605 > 5, we apply the division lemma to 605 and 5, to get
605 = 5 x 121 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 605 is 5
Notice that 5 = HCF(605,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 5, we apply the division lemma to 822 and 5, to get
822 = 5 x 164 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 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 5 and 822 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(822,5) .
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Frequently Asked Questions on HCF of 985, 680, 605, 822 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 985, 680, 605, 822?
Answer: HCF of 985, 680, 605, 822 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 680, 605, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 680, 605, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.