Highest Common Factor of 414, 265 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 414, 265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 265 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 414, 265 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 414, 265 is 1.
HCF(414, 265) = 1
HCF of 414, 265 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 265 is 1.
Highest Common Factor of 414,265 is 1
Step 1: Since 414 > 265, we apply the division lemma to 414 and 265, to get
414 = 265 x 1 + 149
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 149 and 265, to get
265 = 149 x 1 + 116
Step 3: We consider the new divisor 149 and the new remainder 116, and apply the division lemma to get
149 = 116 x 1 + 33
We consider the new divisor 116 and the new remainder 33,and apply the division lemma to get
116 = 33 x 3 + 17
We consider the new divisor 33 and the new remainder 17,and apply the division lemma to get
33 = 17 x 1 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 414 and 265 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(33,17) = HCF(116,33) = HCF(149,116) = HCF(265,149) = HCF(414,265) .
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Frequently Asked Questions on HCF of 414, 265 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 414, 265?
Answer: HCF of 414, 265 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 265 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
