Highest Common Factor of 448, 722, 674 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 448, 722, 674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 722, 674 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 448, 722, 674 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 448, 722, 674 is 2.
HCF(448, 722, 674) = 2
HCF of 448, 722, 674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 722, 674 is 2.
Highest Common Factor of 448,722,674 is 2
Step 1: Since 722 > 448, we apply the division lemma to 722 and 448, to get
722 = 448 x 1 + 274
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 274 and 448, to get
448 = 274 x 1 + 174
Step 3: We consider the new divisor 274 and the new remainder 174, and apply the division lemma to get
274 = 174 x 1 + 100
We consider the new divisor 174 and the new remainder 100,and apply the division lemma to get
174 = 100 x 1 + 74
We consider the new divisor 100 and the new remainder 74,and apply the division lemma to get
100 = 74 x 1 + 26
We consider the new divisor 74 and the new remainder 26,and apply the division lemma to get
74 = 26 x 2 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 448 and 722 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(74,26) = HCF(100,74) = HCF(174,100) = HCF(274,174) = HCF(448,274) = HCF(722,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 674 > 2, we apply the division lemma to 674 and 2, to get
674 = 2 x 337 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 674 is 2
Notice that 2 = HCF(674,2) .
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Frequently Asked Questions on HCF of 448, 722, 674 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 448, 722, 674?
Answer: HCF of 448, 722, 674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 722, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 722, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.