Highest Common Factor of 5736, 1678 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 5736, 1678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5736, 1678 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 5736, 1678 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 5736, 1678 is 2.
HCF(5736, 1678) = 2
HCF of 5736, 1678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5736, 1678 is 2.
Highest Common Factor of 5736,1678 is 2
Step 1: Since 5736 > 1678, we apply the division lemma to 5736 and 1678, to get
5736 = 1678 x 3 + 702
Step 2: Since the reminder 1678 ≠ 0, we apply division lemma to 702 and 1678, to get
1678 = 702 x 2 + 274
Step 3: We consider the new divisor 702 and the new remainder 274, and apply the division lemma to get
702 = 274 x 2 + 154
We consider the new divisor 274 and the new remainder 154,and apply the division lemma to get
274 = 154 x 1 + 120
We consider the new divisor 154 and the new remainder 120,and apply the division lemma to get
154 = 120 x 1 + 34
We consider the new divisor 120 and the new remainder 34,and apply the division lemma to get
120 = 34 x 3 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5736 and 1678 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(120,34) = HCF(154,120) = HCF(274,154) = HCF(702,274) = HCF(1678,702) = HCF(5736,1678) .
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Frequently Asked Questions on HCF of 5736, 1678 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 5736, 1678?
Answer: HCF of 5736, 1678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5736, 1678 using Euclid's Algorithm?
Answer: For arbitrary numbers 5736, 1678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
