Highest Common Factor of 870, 760, 852 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 870, 760, 852 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 760, 852 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 870, 760, 852 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 870, 760, 852 is 2.
HCF(870, 760, 852) = 2
HCF of 870, 760, 852 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 760, 852 is 2.
Highest Common Factor of 870,760,852 is 2
Step 1: Since 870 > 760, we apply the division lemma to 870 and 760, to get
870 = 760 x 1 + 110
Step 2: Since the reminder 760 ≠ 0, we apply division lemma to 110 and 760, to get
760 = 110 x 6 + 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 870 and 760 is 10
Notice that 10 = HCF(100,10) = HCF(110,100) = HCF(760,110) = HCF(870,760) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 852 > 10, we apply the division lemma to 852 and 10, to get
852 = 10 x 85 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 852 is 2
Notice that 2 = HCF(10,2) = HCF(852,10) .
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Frequently Asked Questions on HCF of 870, 760, 852 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 870, 760, 852?
Answer: HCF of 870, 760, 852 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 760, 852 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 760, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
