Highest Common Factor of 400, 1846, 3713 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 400, 1846, 3713 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 1846, 3713 is 1 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 400, 1846, 3713 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 400, 1846, 3713 is 1.
HCF(400, 1846, 3713) = 1
HCF of 400, 1846, 3713 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 1846, 3713 is 1.
Highest Common Factor of 400,1846,3713 is 1
Step 1: Since 1846 > 400, we apply the division lemma to 1846 and 400, to get
1846 = 400 x 4 + 246
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 246 and 400, to get
400 = 246 x 1 + 154
Step 3: We consider the new divisor 246 and the new remainder 154, and apply the division lemma to get
246 = 154 x 1 + 92
We consider the new divisor 154 and the new remainder 92,and apply the division lemma to get
154 = 92 x 1 + 62
We consider the new divisor 92 and the new remainder 62,and apply the division lemma to get
92 = 62 x 1 + 30
We consider the new divisor 62 and the new remainder 30,and apply the division lemma to get
62 = 30 x 2 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 400 and 1846 is 2
Notice that 2 = HCF(30,2) = HCF(62,30) = HCF(92,62) = HCF(154,92) = HCF(246,154) = HCF(400,246) = HCF(1846,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3713 > 2, we apply the division lemma to 3713 and 2, to get
3713 = 2 x 1856 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 3713 is 1
Notice that 1 = HCF(2,1) = HCF(3713,2) .
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Frequently Asked Questions on HCF of 400, 1846, 3713 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 400, 1846, 3713?
Answer: HCF of 400, 1846, 3713 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 1846, 3713 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 1846, 3713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.