Highest Common Factor of 322, 448, 780 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 322, 448, 780 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 448, 780 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 322, 448, 780 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 322, 448, 780 is 2.
HCF(322, 448, 780) = 2
HCF of 322, 448, 780 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 448, 780 is 2.
Highest Common Factor of 322,448,780 is 2
Step 1: Since 448 > 322, we apply the division lemma to 448 and 322, to get
448 = 322 x 1 + 126
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 126 and 322, to get
322 = 126 x 2 + 70
Step 3: We consider the new divisor 126 and the new remainder 70, and apply the division lemma to get
126 = 70 x 1 + 56
We consider the new divisor 70 and the new remainder 56,and apply the division lemma to get
70 = 56 x 1 + 14
We consider the new divisor 56 and the new remainder 14,and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 322 and 448 is 14
Notice that 14 = HCF(56,14) = HCF(70,56) = HCF(126,70) = HCF(322,126) = HCF(448,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 780 > 14, we apply the division lemma to 780 and 14, to get
780 = 14 x 55 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 780 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(780,14) .
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Frequently Asked Questions on HCF of 322, 448, 780 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 322, 448, 780?
Answer: HCF of 322, 448, 780 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 448, 780 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 448, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.