Highest Common Factor of 786, 67904 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 786, 67904 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 786, 67904 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 786, 67904 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 786, 67904 is 2.
HCF(786, 67904) = 2
HCF of 786, 67904 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 786, 67904 is 2.
Highest Common Factor of 786,67904 is 2
Step 1: Since 67904 > 786, we apply the division lemma to 67904 and 786, to get
67904 = 786 x 86 + 308
Step 2: Since the reminder 786 ≠ 0, we apply division lemma to 308 and 786, to get
786 = 308 x 2 + 170
Step 3: We consider the new divisor 308 and the new remainder 170, and apply the division lemma to get
308 = 170 x 1 + 138
We consider the new divisor 170 and the new remainder 138,and apply the division lemma to get
170 = 138 x 1 + 32
We consider the new divisor 138 and the new remainder 32,and apply the division lemma to get
138 = 32 x 4 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 786 and 67904 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(138,32) = HCF(170,138) = HCF(308,170) = HCF(786,308) = HCF(67904,786) .
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Frequently Asked Questions on HCF of 786, 67904 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 786, 67904?
Answer: HCF of 786, 67904 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 786, 67904 using Euclid's Algorithm?
Answer: For arbitrary numbers 786, 67904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.