Highest Common Factor of 969, 47382 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 969, 47382 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 969, 47382 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 969, 47382 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 969, 47382 is 3.
HCF(969, 47382) = 3
HCF of 969, 47382 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 969, 47382 is 3.
Highest Common Factor of 969,47382 is 3
Step 1: Since 47382 > 969, we apply the division lemma to 47382 and 969, to get
47382 = 969 x 48 + 870
Step 2: Since the reminder 969 ≠ 0, we apply division lemma to 870 and 969, to get
969 = 870 x 1 + 99
Step 3: We consider the new divisor 870 and the new remainder 99, and apply the division lemma to get
870 = 99 x 8 + 78
We consider the new divisor 99 and the new remainder 78,and apply the division lemma to get
99 = 78 x 1 + 21
We consider the new divisor 78 and the new remainder 21,and apply the division lemma to get
78 = 21 x 3 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 969 and 47382 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) = HCF(99,78) = HCF(870,99) = HCF(969,870) = HCF(47382,969) .
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Frequently Asked Questions on HCF of 969, 47382 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 969, 47382?
Answer: HCF of 969, 47382 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 969, 47382 using Euclid's Algorithm?
Answer: For arbitrary numbers 969, 47382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.