Highest Common Factor of 254, 412, 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 254, 412, 870 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 254, 412, 870 is 2 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 254, 412, 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 254, 412, 870 is 2.
HCF(254, 412, 870) = 2
HCF of 254, 412, 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 254, 412, 870 is 2.
Highest Common Factor of 254,412,870 is 2
Step 1: Since 412 > 254, we apply the division lemma to 412 and 254, to get
412 = 254 x 1 + 158
Step 2: Since the reminder 254 ≠ 0, we apply division lemma to 158 and 254, to get
254 = 158 x 1 + 96
Step 3: We consider the new divisor 158 and the new remainder 96, and apply the division lemma to get
158 = 96 x 1 + 62
We consider the new divisor 96 and the new remainder 62,and apply the division lemma to get
96 = 62 x 1 + 34
We consider the new divisor 62 and the new remainder 34,and apply the division lemma to get
62 = 34 x 1 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 254 and 412 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(62,34) = HCF(96,62) = HCF(158,96) = HCF(254,158) = HCF(412,254) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 2, we apply the division lemma to 870 and 2, to get
870 = 2 x 435 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 870 is 2
Notice that 2 = HCF(870,2) .
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Frequently Asked Questions on HCF of 254, 412, 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 254, 412, 870?
Answer: HCF of 254, 412, 870 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 254, 412, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 254, 412, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.