Highest Common Factor of 774, 448, 698 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 774, 448, 698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 448, 698 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 774, 448, 698 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 774, 448, 698 is 2.
HCF(774, 448, 698) = 2
HCF of 774, 448, 698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 448, 698 is 2.
Highest Common Factor of 774,448,698 is 2
Step 1: Since 774 > 448, we apply the division lemma to 774 and 448, to get
774 = 448 x 1 + 326
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 326 and 448, to get
448 = 326 x 1 + 122
Step 3: We consider the new divisor 326 and the new remainder 122, and apply the division lemma to get
326 = 122 x 2 + 82
We consider the new divisor 122 and the new remainder 82,and apply the division lemma to get
122 = 82 x 1 + 40
We consider the new divisor 82 and the new remainder 40,and apply the division lemma to get
82 = 40 x 2 + 2
We consider the new divisor 40 and the new remainder 2,and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 774 and 448 is 2
Notice that 2 = HCF(40,2) = HCF(82,40) = HCF(122,82) = HCF(326,122) = HCF(448,326) = HCF(774,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 2, we apply the division lemma to 698 and 2, to get
698 = 2 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 698 is 2
Notice that 2 = HCF(698,2) .
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Frequently Asked Questions on HCF of 774, 448, 698 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 774, 448, 698?
Answer: HCF of 774, 448, 698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 448, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 448, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.