Highest Common Factor of 654, 173, 142 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 654, 173, 142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 173, 142 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 654, 173, 142 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 654, 173, 142 is 1.
HCF(654, 173, 142) = 1
HCF of 654, 173, 142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 173, 142 is 1.
Highest Common Factor of 654,173,142 is 1
Step 1: Since 654 > 173, we apply the division lemma to 654 and 173, to get
654 = 173 x 3 + 135
Step 2: Since the reminder 173 ≠ 0, we apply division lemma to 135 and 173, to get
173 = 135 x 1 + 38
Step 3: We consider the new divisor 135 and the new remainder 38, and apply the division lemma to get
135 = 38 x 3 + 21
We consider the new divisor 38 and the new remainder 21,and apply the division lemma to get
38 = 21 x 1 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 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 654 and 173 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(38,21) = HCF(135,38) = HCF(173,135) = HCF(654,173) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 142 > 1, we apply the division lemma to 142 and 1, to get
142 = 1 x 142 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 142 is 1
Notice that 1 = HCF(142,1) .
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Frequently Asked Questions on HCF of 654, 173, 142 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 654, 173, 142?
Answer: HCF of 654, 173, 142 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 173, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 173, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.