Highest Common Factor of 783, 1984 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 783, 1984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 783, 1984 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 783, 1984 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 783, 1984 is 1.
HCF(783, 1984) = 1
HCF of 783, 1984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 783, 1984 is 1.
Highest Common Factor of 783,1984 is 1
Step 1: Since 1984 > 783, we apply the division lemma to 1984 and 783, to get
1984 = 783 x 2 + 418
Step 2: Since the reminder 783 ≠ 0, we apply division lemma to 418 and 783, to get
783 = 418 x 1 + 365
Step 3: We consider the new divisor 418 and the new remainder 365, and apply the division lemma to get
418 = 365 x 1 + 53
We consider the new divisor 365 and the new remainder 53,and apply the division lemma to get
365 = 53 x 6 + 47
We consider the new divisor 53 and the new remainder 47,and apply the division lemma to get
53 = 47 x 1 + 6
We consider the new divisor 47 and the new remainder 6,and apply the division lemma to get
47 = 6 x 7 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 783 and 1984 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(47,6) = HCF(53,47) = HCF(365,53) = HCF(418,365) = HCF(783,418) = HCF(1984,783) .
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Frequently Asked Questions on HCF of 783, 1984 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 783, 1984?
Answer: HCF of 783, 1984 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 783, 1984 using Euclid's Algorithm?
Answer: For arbitrary numbers 783, 1984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.