Highest Common Factor of 297, 708, 674, 38 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 297, 708, 674, 38 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 297, 708, 674, 38 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 297, 708, 674, 38 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 297, 708, 674, 38 is 1.
HCF(297, 708, 674, 38) = 1
HCF of 297, 708, 674, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 297, 708, 674, 38 is 1.
Highest Common Factor of 297,708,674,38 is 1
Step 1: Since 708 > 297, we apply the division lemma to 708 and 297, to get
708 = 297 x 2 + 114
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 114 and 297, to get
297 = 114 x 2 + 69
Step 3: We consider the new divisor 114 and the new remainder 69, and apply the division lemma to get
114 = 69 x 1 + 45
We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 297 and 708 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(114,69) = HCF(297,114) = HCF(708,297) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 674 > 3, we apply the division lemma to 674 and 3, to get
674 = 3 x 224 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 674 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(674,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 1, we apply the division lemma to 38 and 1, to get
38 = 1 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 38 is 1
Notice that 1 = HCF(38,1) .
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Frequently Asked Questions on HCF of 297, 708, 674, 38 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 297, 708, 674, 38?
Answer: HCF of 297, 708, 674, 38 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 297, 708, 674, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 297, 708, 674, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.