Highest Common Factor of 802, 316, 638 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 802, 316, 638 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 802, 316, 638 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 802, 316, 638 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 802, 316, 638 is 2.
HCF(802, 316, 638) = 2
HCF of 802, 316, 638 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 802, 316, 638 is 2.
Highest Common Factor of 802,316,638 is 2
Step 1: Since 802 > 316, we apply the division lemma to 802 and 316, to get
802 = 316 x 2 + 170
Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 170 and 316, to get
316 = 170 x 1 + 146
Step 3: We consider the new divisor 170 and the new remainder 146, and apply the division lemma to get
170 = 146 x 1 + 24
We consider the new divisor 146 and the new remainder 24,and apply the division lemma to get
146 = 24 x 6 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 802 and 316 is 2
Notice that 2 = HCF(24,2) = HCF(146,24) = HCF(170,146) = HCF(316,170) = HCF(802,316) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 638 > 2, we apply the division lemma to 638 and 2, to get
638 = 2 x 319 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 638 is 2
Notice that 2 = HCF(638,2) .
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Frequently Asked Questions on HCF of 802, 316, 638 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 802, 316, 638?
Answer: HCF of 802, 316, 638 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 802, 316, 638 using Euclid's Algorithm?
Answer: For arbitrary numbers 802, 316, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.