Highest Common Factor of 265, 954, 414 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 265, 954, 414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 265, 954, 414 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 265, 954, 414 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 265, 954, 414 is 1.
HCF(265, 954, 414) = 1
HCF of 265, 954, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 265, 954, 414 is 1.
Highest Common Factor of 265,954,414 is 1
Step 1: Since 954 > 265, we apply the division lemma to 954 and 265, to get
954 = 265 x 3 + 159
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 159 and 265, to get
265 = 159 x 1 + 106
Step 3: We consider the new divisor 159 and the new remainder 106, and apply the division lemma to get
159 = 106 x 1 + 53
We consider the new divisor 106 and the new remainder 53, and apply the division lemma to get
106 = 53 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 53, the HCF of 265 and 954 is 53
Notice that 53 = HCF(106,53) = HCF(159,106) = HCF(265,159) = HCF(954,265) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 53, we apply the division lemma to 414 and 53, to get
414 = 53 x 7 + 43
Step 2: Since the reminder 53 ≠ 0, we apply division lemma to 43 and 53, to get
53 = 43 x 1 + 10
Step 3: We consider the new divisor 43 and the new remainder 10, and apply the division lemma to get
43 = 10 x 4 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 53 and 414 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(43,10) = HCF(53,43) = HCF(414,53) .
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Frequently Asked Questions on HCF of 265, 954, 414 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 265, 954, 414?
Answer: HCF of 265, 954, 414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 265, 954, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 265, 954, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.