Highest Common Factor of 880, 696, 83 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 880, 696, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 880, 696, 83 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 880, 696, 83 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 880, 696, 83 is 1.
HCF(880, 696, 83) = 1
HCF of 880, 696, 83 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 880, 696, 83 is 1.
Highest Common Factor of 880,696,83 is 1
Step 1: Since 880 > 696, we apply the division lemma to 880 and 696, to get
880 = 696 x 1 + 184
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 184 and 696, to get
696 = 184 x 3 + 144
Step 3: We consider the new divisor 184 and the new remainder 144, and apply the division lemma to get
184 = 144 x 1 + 40
We consider the new divisor 144 and the new remainder 40,and apply the division lemma to get
144 = 40 x 3 + 24
We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get
40 = 24 x 1 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 880 and 696 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(144,40) = HCF(184,144) = HCF(696,184) = HCF(880,696) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83 > 8, we apply the division lemma to 83 and 8, to get
83 = 8 x 10 + 3
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 3 and 8, to get
8 = 3 x 2 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 8 and 83 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(83,8) .
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Frequently Asked Questions on HCF of 880, 696, 83 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 880, 696, 83?
Answer: HCF of 880, 696, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 880, 696, 83 using Euclid's Algorithm?
Answer: For arbitrary numbers 880, 696, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.