Highest Common Factor of 269, 699, 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 269, 699, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 269, 699, 664 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 269, 699, 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 269, 699, 664 is 1.
HCF(269, 699, 664) = 1
HCF of 269, 699, 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 269, 699, 664 is 1.
Highest Common Factor of 269,699,664 is 1
Step 1: Since 699 > 269, we apply the division lemma to 699 and 269, to get
699 = 269 x 2 + 161
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 161 and 269, to get
269 = 161 x 1 + 108
Step 3: We consider the new divisor 161 and the new remainder 108, and apply the division lemma to get
161 = 108 x 1 + 53
We consider the new divisor 108 and the new remainder 53,and apply the division lemma to get
108 = 53 x 2 + 2
We consider the new divisor 53 and the new remainder 2,and apply the division lemma to get
53 = 2 x 26 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 269 and 699 is 1
Notice that 1 = HCF(2,1) = HCF(53,2) = HCF(108,53) = HCF(161,108) = HCF(269,161) = HCF(699,269) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get
664 = 1 x 664 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1
Notice that 1 = HCF(664,1) .
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Frequently Asked Questions on HCF of 269, 699, 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 269, 699, 664?
Answer: HCF of 269, 699, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 269, 699, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 269, 699, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
