Highest Common Factor of 208, 960, 299 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, 960, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 960, 299 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, 960, 299 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, 960, 299 is 1.
HCF(208, 960, 299) = 1
HCF of 208, 960, 299 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, 960, 299 is 1.
Highest Common Factor of 208,960,299 is 1
Step 1: Since 960 > 208, we apply the division lemma to 960 and 208, to get
960 = 208 x 4 + 128
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 128 and 208, to get
208 = 128 x 1 + 80
Step 3: We consider the new divisor 128 and the new remainder 80, and apply the division lemma to get
128 = 80 x 1 + 48
We consider the new divisor 80 and the new remainder 48,and apply the division lemma to get
80 = 48 x 1 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 208 and 960 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(80,48) = HCF(128,80) = HCF(208,128) = HCF(960,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 299 > 16, we apply the division lemma to 299 and 16, to get
299 = 16 x 18 + 11
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 11 and 16, to get
16 = 11 x 1 + 5
Step 3: We consider the new divisor 11 and the new remainder 5, and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 299 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(299,16) .
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Frequently Asked Questions on HCF of 208, 960, 299 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, 960, 299?
Answer: HCF of 208, 960, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 960, 299 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 960, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.