Highest Common Factor of 1906, 4972 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 1906, 4972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1906, 4972 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 1906, 4972 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 1906, 4972 is 2.
HCF(1906, 4972) = 2
HCF of 1906, 4972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1906, 4972 is 2.
Highest Common Factor of 1906,4972 is 2
Step 1: Since 4972 > 1906, we apply the division lemma to 4972 and 1906, to get
4972 = 1906 x 2 + 1160
Step 2: Since the reminder 1906 ≠ 0, we apply division lemma to 1160 and 1906, to get
1906 = 1160 x 1 + 746
Step 3: We consider the new divisor 1160 and the new remainder 746, and apply the division lemma to get
1160 = 746 x 1 + 414
We consider the new divisor 746 and the new remainder 414,and apply the division lemma to get
746 = 414 x 1 + 332
We consider the new divisor 414 and the new remainder 332,and apply the division lemma to get
414 = 332 x 1 + 82
We consider the new divisor 332 and the new remainder 82,and apply the division lemma to get
332 = 82 x 4 + 4
We consider the new divisor 82 and the new remainder 4,and apply the division lemma to get
82 = 4 x 20 + 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 1906 and 4972 is 2
Notice that 2 = HCF(4,2) = HCF(82,4) = HCF(332,82) = HCF(414,332) = HCF(746,414) = HCF(1160,746) = HCF(1906,1160) = HCF(4972,1906) .
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Frequently Asked Questions on HCF of 1906, 4972 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 1906, 4972?
Answer: HCF of 1906, 4972 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1906, 4972 using Euclid's Algorithm?
Answer: For arbitrary numbers 1906, 4972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.