Highest Common Factor of 261, 37683 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 261, 37683 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 261, 37683 is 9 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 261, 37683 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 261, 37683 is 9.
HCF(261, 37683) = 9
HCF of 261, 37683 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 261, 37683 is 9.
Highest Common Factor of 261,37683 is 9
Step 1: Since 37683 > 261, we apply the division lemma to 37683 and 261, to get
37683 = 261 x 144 + 99
Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 99 and 261, to get
261 = 99 x 2 + 63
Step 3: We consider the new divisor 99 and the new remainder 63, and apply the division lemma to get
99 = 63 x 1 + 36
We consider the new divisor 63 and the new remainder 36,and apply the division lemma to get
63 = 36 x 1 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 261 and 37683 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(63,36) = HCF(99,63) = HCF(261,99) = HCF(37683,261) .
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Frequently Asked Questions on HCF of 261, 37683 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 261, 37683?
Answer: HCF of 261, 37683 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 261, 37683 using Euclid's Algorithm?
Answer: For arbitrary numbers 261, 37683 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.