Highest Common Factor of 545, 861, 342 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 545, 861, 342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 545, 861, 342 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 545, 861, 342 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 545, 861, 342 is 1.
HCF(545, 861, 342) = 1
HCF of 545, 861, 342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 545, 861, 342 is 1.
Highest Common Factor of 545,861,342 is 1
Step 1: Since 861 > 545, we apply the division lemma to 861 and 545, to get
861 = 545 x 1 + 316
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 316 and 545, to get
545 = 316 x 1 + 229
Step 3: We consider the new divisor 316 and the new remainder 229, and apply the division lemma to get
316 = 229 x 1 + 87
We consider the new divisor 229 and the new remainder 87,and apply the division lemma to get
229 = 87 x 2 + 55
We consider the new divisor 87 and the new remainder 55,and apply the division lemma to get
87 = 55 x 1 + 32
We consider the new divisor 55 and the new remainder 32,and apply the division lemma to get
55 = 32 x 1 + 23
We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get
32 = 23 x 1 + 9
We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get
23 = 9 x 2 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 545 and 861 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(55,32) = HCF(87,55) = HCF(229,87) = HCF(316,229) = HCF(545,316) = HCF(861,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get
342 = 1 x 342 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1
Notice that 1 = HCF(342,1) .
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Frequently Asked Questions on HCF of 545, 861, 342 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 545, 861, 342?
Answer: HCF of 545, 861, 342 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 545, 861, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 545, 861, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
