Highest Common Factor of 646, 1122, 8222 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 646, 1122, 8222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 646, 1122, 8222 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 646, 1122, 8222 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 646, 1122, 8222 is 2.
HCF(646, 1122, 8222) = 2
HCF of 646, 1122, 8222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 646, 1122, 8222 is 2.
Highest Common Factor of 646,1122,8222 is 2
Step 1: Since 1122 > 646, we apply the division lemma to 1122 and 646, to get
1122 = 646 x 1 + 476
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 476 and 646, to get
646 = 476 x 1 + 170
Step 3: We consider the new divisor 476 and the new remainder 170, and apply the division lemma to get
476 = 170 x 2 + 136
We consider the new divisor 170 and the new remainder 136,and apply the division lemma to get
170 = 136 x 1 + 34
We consider the new divisor 136 and the new remainder 34,and apply the division lemma to get
136 = 34 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 646 and 1122 is 34
Notice that 34 = HCF(136,34) = HCF(170,136) = HCF(476,170) = HCF(646,476) = HCF(1122,646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8222 > 34, we apply the division lemma to 8222 and 34, to get
8222 = 34 x 241 + 28
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 28 and 34, to get
34 = 28 x 1 + 6
Step 3: We consider the new divisor 28 and the new remainder 6, and apply the division lemma to get
28 = 6 x 4 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 34 and 8222 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(8222,34) .
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Frequently Asked Questions on HCF of 646, 1122, 8222 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 646, 1122, 8222?
Answer: HCF of 646, 1122, 8222 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 646, 1122, 8222 using Euclid's Algorithm?
Answer: For arbitrary numbers 646, 1122, 8222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.