Highest Common Factor of 208, 416, 929 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, 416, 929 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 416, 929 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, 416, 929 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, 416, 929 is 1.
HCF(208, 416, 929) = 1
HCF of 208, 416, 929 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, 416, 929 is 1.
Highest Common Factor of 208,416,929 is 1
Step 1: Since 416 > 208, we apply the division lemma to 416 and 208, to get
416 = 208 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 208, the HCF of 208 and 416 is 208
Notice that 208 = HCF(416,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 929 > 208, we apply the division lemma to 929 and 208, to get
929 = 208 x 4 + 97
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 97 and 208, to get
208 = 97 x 2 + 14
Step 3: We consider the new divisor 97 and the new remainder 14, and apply the division lemma to get
97 = 14 x 6 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 208 and 929 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(97,14) = HCF(208,97) = HCF(929,208) .
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Frequently Asked Questions on HCF of 208, 416, 929 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, 416, 929?
Answer: HCF of 208, 416, 929 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 416, 929 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 416, 929 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.