Highest Common Factor of 210, 252, 870 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 210, 252, 870 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 252, 870 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 210, 252, 870 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 210, 252, 870 is 6.
HCF(210, 252, 870) = 6
HCF of 210, 252, 870 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 252, 870 is 6.
Highest Common Factor of 210,252,870 is 6
Step 1: Since 252 > 210, we apply the division lemma to 252 and 210, to get
252 = 210 x 1 + 42
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 42 and 210, to get
210 = 42 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 210 and 252 is 42
Notice that 42 = HCF(210,42) = HCF(252,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 42, we apply the division lemma to 870 and 42, to get
870 = 42 x 20 + 30
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 30 and 42, to get
42 = 30 x 1 + 12
Step 3: We consider the new divisor 30 and the new remainder 12, and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 42 and 870 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(870,42) .
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Frequently Asked Questions on HCF of 210, 252, 870 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 210, 252, 870?
Answer: HCF of 210, 252, 870 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 252, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 252, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.