Highest Common Factor of 778, 980, 462 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 778, 980, 462 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 980, 462 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 778, 980, 462 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 778, 980, 462 is 2.
HCF(778, 980, 462) = 2
HCF of 778, 980, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 980, 462 is 2.
Highest Common Factor of 778,980,462 is 2
Step 1: Since 980 > 778, we apply the division lemma to 980 and 778, to get
980 = 778 x 1 + 202
Step 2: Since the reminder 778 ≠ 0, we apply division lemma to 202 and 778, to get
778 = 202 x 3 + 172
Step 3: We consider the new divisor 202 and the new remainder 172, and apply the division lemma to get
202 = 172 x 1 + 30
We consider the new divisor 172 and the new remainder 30,and apply the division lemma to get
172 = 30 x 5 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 778 and 980 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(172,30) = HCF(202,172) = HCF(778,202) = HCF(980,778) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 2, we apply the division lemma to 462 and 2, to get
462 = 2 x 231 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 462 is 2
Notice that 2 = HCF(462,2) .
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Frequently Asked Questions on HCF of 778, 980, 462 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 778, 980, 462?
Answer: HCF of 778, 980, 462 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 980, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 980, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.