Highest Common Factor of 981, 61674 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 981, 61674 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 981, 61674 is 3 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 981, 61674 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 981, 61674 is 3.
HCF(981, 61674) = 3
HCF of 981, 61674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 981, 61674 is 3.
Highest Common Factor of 981,61674 is 3
Step 1: Since 61674 > 981, we apply the division lemma to 61674 and 981, to get
61674 = 981 x 62 + 852
Step 2: Since the reminder 981 ≠ 0, we apply division lemma to 852 and 981, to get
981 = 852 x 1 + 129
Step 3: We consider the new divisor 852 and the new remainder 129, and apply the division lemma to get
852 = 129 x 6 + 78
We consider the new divisor 129 and the new remainder 78,and apply the division lemma to get
129 = 78 x 1 + 51
We consider the new divisor 78 and the new remainder 51,and apply the division lemma to get
78 = 51 x 1 + 27
We consider the new divisor 51 and the new remainder 27,and apply the division lemma to get
51 = 27 x 1 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 981 and 61674 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(51,27) = HCF(78,51) = HCF(129,78) = HCF(852,129) = HCF(981,852) = HCF(61674,981) .
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Frequently Asked Questions on HCF of 981, 61674 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 981, 61674?
Answer: HCF of 981, 61674 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 981, 61674 using Euclid's Algorithm?
Answer: For arbitrary numbers 981, 61674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.