Highest Common Factor of 209, 322, 678, 752 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 209, 322, 678, 752 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 322, 678, 752 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 209, 322, 678, 752 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 209, 322, 678, 752 is 1.
HCF(209, 322, 678, 752) = 1
HCF of 209, 322, 678, 752 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 322, 678, 752 is 1.
Highest Common Factor of 209,322,678,752 is 1
Step 1: Since 322 > 209, we apply the division lemma to 322 and 209, to get
322 = 209 x 1 + 113
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 113 and 209, to get
209 = 113 x 1 + 96
Step 3: We consider the new divisor 113 and the new remainder 96, and apply the division lemma to get
113 = 96 x 1 + 17
We consider the new divisor 96 and the new remainder 17,and apply the division lemma to get
96 = 17 x 5 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 209 and 322 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(96,17) = HCF(113,96) = HCF(209,113) = HCF(322,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get
678 = 1 x 678 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1
Notice that 1 = HCF(678,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 752 > 1, we apply the division lemma to 752 and 1, to get
752 = 1 x 752 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 752 is 1
Notice that 1 = HCF(752,1) .
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Frequently Asked Questions on HCF of 209, 322, 678, 752 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 209, 322, 678, 752?
Answer: HCF of 209, 322, 678, 752 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 322, 678, 752 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 322, 678, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.