Highest Common Factor of 634, 280, 669, 683 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 634, 280, 669, 683 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 634, 280, 669, 683 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 634, 280, 669, 683 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 634, 280, 669, 683 is 1.
HCF(634, 280, 669, 683) = 1
HCF of 634, 280, 669, 683 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 634, 280, 669, 683 is 1.
Highest Common Factor of 634,280,669,683 is 1
Step 1: Since 634 > 280, we apply the division lemma to 634 and 280, to get
634 = 280 x 2 + 74
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 74 and 280, to get
280 = 74 x 3 + 58
Step 3: We consider the new divisor 74 and the new remainder 58, and apply the division lemma to get
74 = 58 x 1 + 16
We consider the new divisor 58 and the new remainder 16,and apply the division lemma to get
58 = 16 x 3 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 634 and 280 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(58,16) = HCF(74,58) = HCF(280,74) = HCF(634,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 669 > 2, we apply the division lemma to 669 and 2, to get
669 = 2 x 334 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 669 is 1
Notice that 1 = HCF(2,1) = HCF(669,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 683 > 1, we apply the division lemma to 683 and 1, to get
683 = 1 x 683 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 683 is 1
Notice that 1 = HCF(683,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 634, 280, 669, 683 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 634, 280, 669, 683?
Answer: HCF of 634, 280, 669, 683 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 634, 280, 669, 683 using Euclid's Algorithm?
Answer: For arbitrary numbers 634, 280, 669, 683 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.