Highest Common Factor of 786, 3648 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, 3648 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 786, 3648 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 786, 3648 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, 3648 is 6.
HCF(786, 3648) = 6
HCF of 786, 3648 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, 3648 is 6.
Highest Common Factor of 786,3648 is 6
Step 1: Since 3648 > 786, we apply the division lemma to 3648 and 786, to get
3648 = 786 x 4 + 504
Step 2: Since the reminder 786 ≠ 0, we apply division lemma to 504 and 786, to get
786 = 504 x 1 + 282
Step 3: We consider the new divisor 504 and the new remainder 282, and apply the division lemma to get
504 = 282 x 1 + 222
We consider the new divisor 282 and the new remainder 222,and apply the division lemma to get
282 = 222 x 1 + 60
We consider the new divisor 222 and the new remainder 60,and apply the division lemma to get
222 = 60 x 3 + 42
We consider the new divisor 60 and the new remainder 42,and apply the division lemma to get
60 = 42 x 1 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 786 and 3648 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(60,42) = HCF(222,60) = HCF(282,222) = HCF(504,282) = HCF(786,504) = HCF(3648,786) .
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Frequently Asked Questions on HCF of 786, 3648 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, 3648?
Answer: HCF of 786, 3648 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 786, 3648 using Euclid's Algorithm?
Answer: For arbitrary numbers 786, 3648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.