Highest Common Factor of 438, 710, 916 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 438, 710, 916 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 438, 710, 916 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 438, 710, 916 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 438, 710, 916 is 2.
HCF(438, 710, 916) = 2
HCF of 438, 710, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 438, 710, 916 is 2.
Highest Common Factor of 438,710,916 is 2
Step 1: Since 710 > 438, we apply the division lemma to 710 and 438, to get
710 = 438 x 1 + 272
Step 2: Since the reminder 438 ≠ 0, we apply division lemma to 272 and 438, to get
438 = 272 x 1 + 166
Step 3: We consider the new divisor 272 and the new remainder 166, and apply the division lemma to get
272 = 166 x 1 + 106
We consider the new divisor 166 and the new remainder 106,and apply the division lemma to get
166 = 106 x 1 + 60
We consider the new divisor 106 and the new remainder 60,and apply the division lemma to get
106 = 60 x 1 + 46
We consider the new divisor 60 and the new remainder 46,and apply the division lemma to get
60 = 46 x 1 + 14
We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get
46 = 14 x 3 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 438 and 710 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(60,46) = HCF(106,60) = HCF(166,106) = HCF(272,166) = HCF(438,272) = HCF(710,438) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 2, we apply the division lemma to 916 and 2, to get
916 = 2 x 458 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 916 is 2
Notice that 2 = HCF(916,2) .
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Frequently Asked Questions on HCF of 438, 710, 916 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 438, 710, 916?
Answer: HCF of 438, 710, 916 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 438, 710, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 438, 710, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
