Highest Common Factor of 814, 220, 222, 616 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 814, 220, 222, 616 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 220, 222, 616 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 814, 220, 222, 616 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 814, 220, 222, 616 is 2.
HCF(814, 220, 222, 616) = 2
HCF of 814, 220, 222, 616 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 220, 222, 616 is 2.
Highest Common Factor of 814,220,222,616 is 2
Step 1: Since 814 > 220, we apply the division lemma to 814 and 220, to get
814 = 220 x 3 + 154
Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 154 and 220, to get
220 = 154 x 1 + 66
Step 3: We consider the new divisor 154 and the new remainder 66, and apply the division lemma to get
154 = 66 x 2 + 22
We consider the new divisor 66 and the new remainder 22, and apply the division lemma to get
66 = 22 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 814 and 220 is 22
Notice that 22 = HCF(66,22) = HCF(154,66) = HCF(220,154) = HCF(814,220) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 222 > 22, we apply the division lemma to 222 and 22, to get
222 = 22 x 10 + 2
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 2 and 22, to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 222 is 2
Notice that 2 = HCF(22,2) = HCF(222,22) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 616 > 2, we apply the division lemma to 616 and 2, to get
616 = 2 x 308 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 616 is 2
Notice that 2 = HCF(616,2) .
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Frequently Asked Questions on HCF of 814, 220, 222, 616 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 814, 220, 222, 616?
Answer: HCF of 814, 220, 222, 616 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 220, 222, 616 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 220, 222, 616 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.