Highest Common Factor of 852, 1257, 2685 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 852, 1257, 2685 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 1257, 2685 is 3 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 852, 1257, 2685 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 852, 1257, 2685 is 3.
HCF(852, 1257, 2685) = 3
HCF of 852, 1257, 2685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 852, 1257, 2685 is 3.
Highest Common Factor of 852,1257,2685 is 3
Step 1: Since 1257 > 852, we apply the division lemma to 1257 and 852, to get
1257 = 852 x 1 + 405
Step 2: Since the reminder 852 ≠ 0, we apply division lemma to 405 and 852, to get
852 = 405 x 2 + 42
Step 3: We consider the new divisor 405 and the new remainder 42, and apply the division lemma to get
405 = 42 x 9 + 27
We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get
42 = 27 x 1 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 852 and 1257 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(405,42) = HCF(852,405) = HCF(1257,852) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2685 > 3, we apply the division lemma to 2685 and 3, to get
2685 = 3 x 895 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 2685 is 3
Notice that 3 = HCF(2685,3) .
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Frequently Asked Questions on HCF of 852, 1257, 2685 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 852, 1257, 2685?
Answer: HCF of 852, 1257, 2685 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 1257, 2685 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 1257, 2685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.