Highest Common Factor of 870, 330, 67 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, 330, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 330, 67 is 1 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, 330, 67 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, 330, 67 is 1.
HCF(870, 330, 67) = 1
HCF of 870, 330, 67 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, 330, 67 is 1.
Highest Common Factor of 870,330,67 is 1
Step 1: Since 870 > 330, we apply the division lemma to 870 and 330, to get
870 = 330 x 2 + 210
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 210 and 330, to get
330 = 210 x 1 + 120
Step 3: We consider the new divisor 210 and the new remainder 120, and apply the division lemma to get
210 = 120 x 1 + 90
We consider the new divisor 120 and the new remainder 90,and apply the division lemma to get
120 = 90 x 1 + 30
We consider the new divisor 90 and the new remainder 30,and apply the division lemma to get
90 = 30 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 870 and 330 is 30
Notice that 30 = HCF(90,30) = HCF(120,90) = HCF(210,120) = HCF(330,210) = HCF(870,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 30, we apply the division lemma to 67 and 30, to get
67 = 30 x 2 + 7
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 7 and 30, to get
30 = 7 x 4 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 30 and 67 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(30,7) = HCF(67,30) .
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Frequently Asked Questions on HCF of 870, 330, 67 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, 330, 67?
Answer: HCF of 870, 330, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 330, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 330, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.