Highest Common Factor of 354, 538, 889 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, 538, 889 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 538, 889 is 1 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, 538, 889 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, 538, 889 is 1.
HCF(354, 538, 889) = 1
HCF of 354, 538, 889 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, 538, 889 is 1.
Highest Common Factor of 354,538,889 is 1
Step 1: Since 538 > 354, we apply the division lemma to 538 and 354, to get
538 = 354 x 1 + 184
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 184 and 354, to get
354 = 184 x 1 + 170
Step 3: We consider the new divisor 184 and the new remainder 170, and apply the division lemma to get
184 = 170 x 1 + 14
We consider the new divisor 170 and the new remainder 14,and apply the division lemma to get
170 = 14 x 12 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 538 is 2
Notice that 2 = HCF(14,2) = HCF(170,14) = HCF(184,170) = HCF(354,184) = HCF(538,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 889 > 2, we apply the division lemma to 889 and 2, to get
889 = 2 x 444 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 889 is 1
Notice that 1 = HCF(2,1) = HCF(889,2) .
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Frequently Asked Questions on HCF of 354, 538, 889 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, 538, 889?
Answer: HCF of 354, 538, 889 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 538, 889 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 538, 889 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.