Highest Common Factor of 870, 960, 234 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, 960, 234 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 960, 234 is 6 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, 960, 234 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, 960, 234 is 6.
HCF(870, 960, 234) = 6
HCF of 870, 960, 234 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, 960, 234 is 6.
Highest Common Factor of 870,960,234 is 6
Step 1: Since 960 > 870, we apply the division lemma to 960 and 870, to get
960 = 870 x 1 + 90
Step 2: Since the reminder 870 ≠ 0, we apply division lemma to 90 and 870, to get
870 = 90 x 9 + 60
Step 3: We consider the new divisor 90 and the new remainder 60, and apply the division lemma to get
90 = 60 x 1 + 30
We consider the new divisor 60 and the new remainder 30, and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 870 and 960 is 30
Notice that 30 = HCF(60,30) = HCF(90,60) = HCF(870,90) = HCF(960,870) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 234 > 30, we apply the division lemma to 234 and 30, to get
234 = 30 x 7 + 24
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 24 and 30, to get
30 = 24 x 1 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 234 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(234,30) .
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Frequently Asked Questions on HCF of 870, 960, 234 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, 960, 234?
Answer: HCF of 870, 960, 234 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 960, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 960, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.