Highest Common Factor of 78, 468, 992 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 78, 468, 992 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 78, 468, 992 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 78, 468, 992 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 78, 468, 992 is 2.
HCF(78, 468, 992) = 2
HCF of 78, 468, 992 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 78, 468, 992 is 2.
Highest Common Factor of 78,468,992 is 2
Step 1: Since 468 > 78, we apply the division lemma to 468 and 78, to get
468 = 78 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 78 and 468 is 78
Notice that 78 = HCF(468,78) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 992 > 78, we apply the division lemma to 992 and 78, to get
992 = 78 x 12 + 56
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 56 and 78, to get
78 = 56 x 1 + 22
Step 3: We consider the new divisor 56 and the new remainder 22, and apply the division lemma to get
56 = 22 x 2 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 78 and 992 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(56,22) = HCF(78,56) = HCF(992,78) .
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Frequently Asked Questions on HCF of 78, 468, 992 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 78, 468, 992?
Answer: HCF of 78, 468, 992 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 78, 468, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 78, 468, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
