Highest Common Factor of 415, 664 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 415, 664 i.e. 83 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 664 is 83 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 415, 664 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 415, 664 is 83.
HCF(415, 664) = 83
HCF of 415, 664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 664 is 83.
Highest Common Factor of 415,664 is 83
Step 1: Since 664 > 415, we apply the division lemma to 664 and 415, to get
664 = 415 x 1 + 249
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 249 and 415, to get
415 = 249 x 1 + 166
Step 3: We consider the new divisor 249 and the new remainder 166, and apply the division lemma to get
249 = 166 x 1 + 83
We consider the new divisor 166 and the new remainder 83, and apply the division lemma to get
166 = 83 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 83, the HCF of 415 and 664 is 83
Notice that 83 = HCF(166,83) = HCF(249,166) = HCF(415,249) = HCF(664,415) .
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Frequently Asked Questions on HCF of 415, 664 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 415, 664?
Answer: HCF of 415, 664 is 83 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.