Highest Common Factor of 986, 770, 306 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 986, 770, 306 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 770, 306 is 2 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 986, 770, 306 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 986, 770, 306 is 2.
HCF(986, 770, 306) = 2
HCF of 986, 770, 306 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 770, 306 is 2.
Highest Common Factor of 986,770,306 is 2
Step 1: Since 986 > 770, we apply the division lemma to 986 and 770, to get
986 = 770 x 1 + 216
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 216 and 770, to get
770 = 216 x 3 + 122
Step 3: We consider the new divisor 216 and the new remainder 122, and apply the division lemma to get
216 = 122 x 1 + 94
We consider the new divisor 122 and the new remainder 94,and apply the division lemma to get
122 = 94 x 1 + 28
We consider the new divisor 94 and the new remainder 28,and apply the division lemma to get
94 = 28 x 3 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 986 and 770 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(94,28) = HCF(122,94) = HCF(216,122) = HCF(770,216) = HCF(986,770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 306 > 2, we apply the division lemma to 306 and 2, to get
306 = 2 x 153 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 306 is 2
Notice that 2 = HCF(306,2) .
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Frequently Asked Questions on HCF of 986, 770, 306 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 986, 770, 306?
Answer: HCF of 986, 770, 306 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 770, 306 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 770, 306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.