Highest Common Factor of 134, 654, 420 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 134, 654, 420 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 134, 654, 420 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 134, 654, 420 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 134, 654, 420 is 2.
HCF(134, 654, 420) = 2
HCF of 134, 654, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 134, 654, 420 is 2.
Highest Common Factor of 134,654,420 is 2
Step 1: Since 654 > 134, we apply the division lemma to 654 and 134, to get
654 = 134 x 4 + 118
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 118 and 134, to get
134 = 118 x 1 + 16
Step 3: We consider the new divisor 118 and the new remainder 16, and apply the division lemma to get
118 = 16 x 7 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 134 and 654 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(118,16) = HCF(134,118) = HCF(654,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 420 > 2, we apply the division lemma to 420 and 2, to get
420 = 2 x 210 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 420 is 2
Notice that 2 = HCF(420,2) .
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Frequently Asked Questions on HCF of 134, 654, 420 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 134, 654, 420?
Answer: HCF of 134, 654, 420 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 134, 654, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 134, 654, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.