Highest Common Factor of 70, 294, 864, 434 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 70, 294, 864, 434 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 294, 864, 434 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 70, 294, 864, 434 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 70, 294, 864, 434 is 2.
HCF(70, 294, 864, 434) = 2
HCF of 70, 294, 864, 434 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 294, 864, 434 is 2.
Highest Common Factor of 70,294,864,434 is 2
Step 1: Since 294 > 70, we apply the division lemma to 294 and 70, to get
294 = 70 x 4 + 14
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 14 and 70, to get
70 = 14 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 70 and 294 is 14
Notice that 14 = HCF(70,14) = HCF(294,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 864 > 14, we apply the division lemma to 864 and 14, to get
864 = 14 x 61 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 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 14 and 864 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(864,14) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 434 > 2, we apply the division lemma to 434 and 2, to get
434 = 2 x 217 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 434 is 2
Notice that 2 = HCF(434,2) .
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Frequently Asked Questions on HCF of 70, 294, 864, 434 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 70, 294, 864, 434?
Answer: HCF of 70, 294, 864, 434 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 294, 864, 434 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 294, 864, 434 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.