Highest Common Factor of 870, 189, 720 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, 189, 720 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 189, 720 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 870, 189, 720 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, 189, 720 is 3.
HCF(870, 189, 720) = 3
HCF of 870, 189, 720 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, 189, 720 is 3.
Highest Common Factor of 870,189,720 is 3
Step 1: Since 870 > 189, we apply the division lemma to 870 and 189, to get
870 = 189 x 4 + 114
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 114 and 189, to get
189 = 114 x 1 + 75
Step 3: We consider the new divisor 114 and the new remainder 75, and apply the division lemma to get
114 = 75 x 1 + 39
We consider the new divisor 75 and the new remainder 39,and apply the division lemma to get
75 = 39 x 1 + 36
We consider the new divisor 39 and the new remainder 36,and apply the division lemma to get
39 = 36 x 1 + 3
We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 870 and 189 is 3
Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(75,39) = HCF(114,75) = HCF(189,114) = HCF(870,189) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 720 > 3, we apply the division lemma to 720 and 3, to get
720 = 3 x 240 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 720 is 3
Notice that 3 = HCF(720,3) .
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Frequently Asked Questions on HCF of 870, 189, 720 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, 189, 720?
Answer: HCF of 870, 189, 720 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 189, 720 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 189, 720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.