Highest Common Factor of 354, 874, 810 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 354, 874, 810 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 874, 810 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 354, 874, 810 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 354, 874, 810 is 2.
HCF(354, 874, 810) = 2
HCF of 354, 874, 810 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 874, 810 is 2.
Highest Common Factor of 354,874,810 is 2
Step 1: Since 874 > 354, we apply the division lemma to 874 and 354, to get
874 = 354 x 2 + 166
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 166 and 354, to get
354 = 166 x 2 + 22
Step 3: We consider the new divisor 166 and the new remainder 22, and apply the division lemma to get
166 = 22 x 7 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 874 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(166,22) = HCF(354,166) = HCF(874,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 810 > 2, we apply the division lemma to 810 and 2, to get
810 = 2 x 405 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 810 is 2
Notice that 2 = HCF(810,2) .
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Frequently Asked Questions on HCF of 354, 874, 810 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 354, 874, 810?
Answer: HCF of 354, 874, 810 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 874, 810 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 874, 810 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.