Highest Common Factor of 210, 738, 524 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, 738, 524 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 738, 524 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 210, 738, 524 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, 738, 524 is 2.
HCF(210, 738, 524) = 2
HCF of 210, 738, 524 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, 738, 524 is 2.
Highest Common Factor of 210,738,524 is 2
Step 1: Since 738 > 210, we apply the division lemma to 738 and 210, to get
738 = 210 x 3 + 108
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 108 and 210, to get
210 = 108 x 1 + 102
Step 3: We consider the new divisor 108 and the new remainder 102, and apply the division lemma to get
108 = 102 x 1 + 6
We consider the new divisor 102 and the new remainder 6, and apply the division lemma to get
102 = 6 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 210 and 738 is 6
Notice that 6 = HCF(102,6) = HCF(108,102) = HCF(210,108) = HCF(738,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 524 > 6, we apply the division lemma to 524 and 6, to get
524 = 6 x 87 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 524 is 2
Notice that 2 = HCF(6,2) = HCF(524,6) .
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Frequently Asked Questions on HCF of 210, 738, 524 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, 738, 524?
Answer: HCF of 210, 738, 524 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 738, 524 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 738, 524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.