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 520, 871, 902 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 520, 871, 902 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 520, 871, 902 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 520, 871, 902 is 1.
HCF(520, 871, 902) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 520, 871, 902 is 1.
Step 1: Since 871 > 520, we apply the division lemma to 871 and 520, to get
871 = 520 x 1 + 351
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 351 and 520, to get
520 = 351 x 1 + 169
Step 3: We consider the new divisor 351 and the new remainder 169, and apply the division lemma to get
351 = 169 x 2 + 13
We consider the new divisor 169 and the new remainder 13, and apply the division lemma to get
169 = 13 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 520 and 871 is 13
Notice that 13 = HCF(169,13) = HCF(351,169) = HCF(520,351) = HCF(871,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 902 > 13, we apply the division lemma to 902 and 13, to get
902 = 13 x 69 + 5
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 5 and 13, to get
13 = 5 x 2 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 13 and 902 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(902,13) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 520, 871, 902?
Answer: HCF of 520, 871, 902 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 520, 871, 902 using Euclid's Algorithm?
Answer: For arbitrary numbers 520, 871, 902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.