Highest Common Factor of 208, 532, 264, 269 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 208, 532, 264, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 532, 264, 269 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 208, 532, 264, 269 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 208, 532, 264, 269 is 1.
HCF(208, 532, 264, 269) = 1
HCF of 208, 532, 264, 269 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 208, 532, 264, 269 is 1.
Highest Common Factor of 208,532,264,269 is 1
Step 1: Since 532 > 208, we apply the division lemma to 532 and 208, to get
532 = 208 x 2 + 116
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 116 and 208, to get
208 = 116 x 1 + 92
Step 3: We consider the new divisor 116 and the new remainder 92, and apply the division lemma to get
116 = 92 x 1 + 24
We consider the new divisor 92 and the new remainder 24,and apply the division lemma to get
92 = 24 x 3 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 208 and 532 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(92,24) = HCF(116,92) = HCF(208,116) = HCF(532,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 264 > 4, we apply the division lemma to 264 and 4, to get
264 = 4 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 264 is 4
Notice that 4 = HCF(264,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 269 > 4, we apply the division lemma to 269 and 4, to get
269 = 4 x 67 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 269 is 1
Notice that 1 = HCF(4,1) = HCF(269,4) .
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Frequently Asked Questions on HCF of 208, 532, 264, 269 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 208, 532, 264, 269?
Answer: HCF of 208, 532, 264, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 532, 264, 269 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 532, 264, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.