Highest Common Factor of 616, 407, 505 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 616, 407, 505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 616, 407, 505 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 616, 407, 505 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 616, 407, 505 is 1.
HCF(616, 407, 505) = 1
HCF of 616, 407, 505 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 616, 407, 505 is 1.
Highest Common Factor of 616,407,505 is 1
Step 1: Since 616 > 407, we apply the division lemma to 616 and 407, to get
616 = 407 x 1 + 209
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 209 and 407, to get
407 = 209 x 1 + 198
Step 3: We consider the new divisor 209 and the new remainder 198, and apply the division lemma to get
209 = 198 x 1 + 11
We consider the new divisor 198 and the new remainder 11, and apply the division lemma to get
198 = 11 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 616 and 407 is 11
Notice that 11 = HCF(198,11) = HCF(209,198) = HCF(407,209) = HCF(616,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 505 > 11, we apply the division lemma to 505 and 11, to get
505 = 11 x 45 + 10
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 10 and 11, to get
11 = 10 x 1 + 1
Step 3: We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 505 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(505,11) .
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Frequently Asked Questions on HCF of 616, 407, 505 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 616, 407, 505?
Answer: HCF of 616, 407, 505 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 616, 407, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 616, 407, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
