Highest Common Factor of 210, 530, 351 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 210, 530, 351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 530, 351 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 210, 530, 351 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 210, 530, 351 is 1.
HCF(210, 530, 351) = 1
HCF of 210, 530, 351 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 530, 351 is 1.
Highest Common Factor of 210,530,351 is 1
Step 1: Since 530 > 210, we apply the division lemma to 530 and 210, to get
530 = 210 x 2 + 110
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 110 and 210, to get
210 = 110 x 1 + 100
Step 3: We consider the new divisor 110 and the new remainder 100, and apply the division lemma to get
110 = 100 x 1 + 10
We consider the new divisor 100 and the new remainder 10, and apply the division lemma to get
100 = 10 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 210 and 530 is 10
Notice that 10 = HCF(100,10) = HCF(110,100) = HCF(210,110) = HCF(530,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 351 > 10, we apply the division lemma to 351 and 10, to get
351 = 10 x 35 + 1
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 351 is 1
Notice that 1 = HCF(10,1) = HCF(351,10) .
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Frequently Asked Questions on HCF of 210, 530, 351 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 210, 530, 351?
Answer: HCF of 210, 530, 351 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 530, 351 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 530, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.