Highest Common Factor of 655, 398, 738 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 655, 398, 738 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 398, 738 is 1 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 655, 398, 738 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 655, 398, 738 is 1.
HCF(655, 398, 738) = 1
HCF of 655, 398, 738 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 655, 398, 738 is 1.
Highest Common Factor of 655,398,738 is 1
Step 1: Since 655 > 398, we apply the division lemma to 655 and 398, to get
655 = 398 x 1 + 257
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 257 and 398, to get
398 = 257 x 1 + 141
Step 3: We consider the new divisor 257 and the new remainder 141, and apply the division lemma to get
257 = 141 x 1 + 116
We consider the new divisor 141 and the new remainder 116,and apply the division lemma to get
141 = 116 x 1 + 25
We consider the new divisor 116 and the new remainder 25,and apply the division lemma to get
116 = 25 x 4 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 655 and 398 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(116,25) = HCF(141,116) = HCF(257,141) = HCF(398,257) = HCF(655,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 738 > 1, we apply the division lemma to 738 and 1, to get
738 = 1 x 738 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 738 is 1
Notice that 1 = HCF(738,1) .
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Frequently Asked Questions on HCF of 655, 398, 738 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 655, 398, 738?
Answer: HCF of 655, 398, 738 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 398, 738 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 398, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.