Highest Common Factor of 128, 870, 642 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 128, 870, 642 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 128, 870, 642 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 128, 870, 642 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 128, 870, 642 is 2.
HCF(128, 870, 642) = 2
HCF of 128, 870, 642 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 128, 870, 642 is 2.
Highest Common Factor of 128,870,642 is 2
Step 1: Since 870 > 128, we apply the division lemma to 870 and 128, to get
870 = 128 x 6 + 102
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 102 and 128, to get
128 = 102 x 1 + 26
Step 3: We consider the new divisor 102 and the new remainder 26, and apply the division lemma to get
102 = 26 x 3 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 128 and 870 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(102,26) = HCF(128,102) = HCF(870,128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 642 > 2, we apply the division lemma to 642 and 2, to get
642 = 2 x 321 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 642 is 2
Notice that 2 = HCF(642,2) .
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Frequently Asked Questions on HCF of 128, 870, 642 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 128, 870, 642?
Answer: HCF of 128, 870, 642 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 128, 870, 642 using Euclid's Algorithm?
Answer: For arbitrary numbers 128, 870, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.