Highest Common Factor of 870, 510, 660 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, 510, 660 i.e. 30 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 510, 660 is 30 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, 510, 660 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, 510, 660 is 30.
HCF(870, 510, 660) = 30
HCF of 870, 510, 660 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, 510, 660 is 30.
Highest Common Factor of 870,510,660 is 30
Step 1: Since 870 > 510, we apply the division lemma to 870 and 510, to get
870 = 510 x 1 + 360
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 360 and 510, to get
510 = 360 x 1 + 150
Step 3: We consider the new divisor 360 and the new remainder 150, and apply the division lemma to get
360 = 150 x 2 + 60
We consider the new divisor 150 and the new remainder 60,and apply the division lemma to get
150 = 60 x 2 + 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 510 is 30
Notice that 30 = HCF(60,30) = HCF(150,60) = HCF(360,150) = HCF(510,360) = HCF(870,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 30, we apply the division lemma to 660 and 30, to get
660 = 30 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 30 and 660 is 30
Notice that 30 = HCF(660,30) .
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Frequently Asked Questions on HCF of 870, 510, 660 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, 510, 660?
Answer: HCF of 870, 510, 660 is 30 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 510, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 510, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.