Highest Common Factor of 455, 665, 116 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 455, 665, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 665, 116 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 455, 665, 116 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 455, 665, 116 is 1.
HCF(455, 665, 116) = 1
HCF of 455, 665, 116 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 665, 116 is 1.
Highest Common Factor of 455,665,116 is 1
Step 1: Since 665 > 455, we apply the division lemma to 665 and 455, to get
665 = 455 x 1 + 210
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 210 and 455, to get
455 = 210 x 2 + 35
Step 3: We consider the new divisor 210 and the new remainder 35, and apply the division lemma to get
210 = 35 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 455 and 665 is 35
Notice that 35 = HCF(210,35) = HCF(455,210) = HCF(665,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 35, we apply the division lemma to 116 and 35, to get
116 = 35 x 3 + 11
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 11 and 35, to get
35 = 11 x 3 + 2
Step 3: We consider the new divisor 11 and the new remainder 2, and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 116 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(116,35) .
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Frequently Asked Questions on HCF of 455, 665, 116 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 455, 665, 116?
Answer: HCF of 455, 665, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 665, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 665, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
