Highest Common Factor of 755, 406, 208 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 755, 406, 208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 755, 406, 208 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 755, 406, 208 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 755, 406, 208 is 1.
HCF(755, 406, 208) = 1
HCF of 755, 406, 208 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 755, 406, 208 is 1.
Highest Common Factor of 755,406,208 is 1
Step 1: Since 755 > 406, we apply the division lemma to 755 and 406, to get
755 = 406 x 1 + 349
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 349 and 406, to get
406 = 349 x 1 + 57
Step 3: We consider the new divisor 349 and the new remainder 57, and apply the division lemma to get
349 = 57 x 6 + 7
We consider the new divisor 57 and the new remainder 7,and apply the division lemma to get
57 = 7 x 8 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 755 and 406 is 1
Notice that 1 = HCF(7,1) = HCF(57,7) = HCF(349,57) = HCF(406,349) = HCF(755,406) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 208 > 1, we apply the division lemma to 208 and 1, to get
208 = 1 x 208 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 208 is 1
Notice that 1 = HCF(208,1) .
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Frequently Asked Questions on HCF of 755, 406, 208 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 755, 406, 208?
Answer: HCF of 755, 406, 208 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 755, 406, 208 using Euclid's Algorithm?
Answer: For arbitrary numbers 755, 406, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.