Highest Common Factor of 728, 520, 853 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 728, 520, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 520, 853 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 728, 520, 853 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 728, 520, 853 is 1.
HCF(728, 520, 853) = 1
HCF of 728, 520, 853 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 520, 853 is 1.
Highest Common Factor of 728,520,853 is 1
Step 1: Since 728 > 520, we apply the division lemma to 728 and 520, to get
728 = 520 x 1 + 208
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 208 and 520, to get
520 = 208 x 2 + 104
Step 3: We consider the new divisor 208 and the new remainder 104, and apply the division lemma to get
208 = 104 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 104, the HCF of 728 and 520 is 104
Notice that 104 = HCF(208,104) = HCF(520,208) = HCF(728,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 853 > 104, we apply the division lemma to 853 and 104, to get
853 = 104 x 8 + 21
Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 21 and 104, to get
104 = 21 x 4 + 20
Step 3: We consider the new divisor 21 and the new remainder 20, and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1, and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 104 and 853 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(104,21) = HCF(853,104) .
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Frequently Asked Questions on HCF of 728, 520, 853 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 728, 520, 853?
Answer: HCF of 728, 520, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 520, 853 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 520, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.