Highest Common Factor of 280, 696, 470 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 280, 696, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 280, 696, 470 is 2 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 280, 696, 470 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 280, 696, 470 is 2.
HCF(280, 696, 470) = 2
HCF of 280, 696, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 280, 696, 470 is 2.
Highest Common Factor of 280,696,470 is 2
Step 1: Since 696 > 280, we apply the division lemma to 696 and 280, to get
696 = 280 x 2 + 136
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 136 and 280, to get
280 = 136 x 2 + 8
Step 3: We consider the new divisor 136 and the new remainder 8, and apply the division lemma to get
136 = 8 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 280 and 696 is 8
Notice that 8 = HCF(136,8) = HCF(280,136) = HCF(696,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 8, we apply the division lemma to 470 and 8, to get
470 = 8 x 58 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 470 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(470,8) .
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Frequently Asked Questions on HCF of 280, 696, 470 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 280, 696, 470?
Answer: HCF of 280, 696, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 280, 696, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 280, 696, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.