Highest Common Factor of 974, 704, 415 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 974, 704, 415 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 704, 415 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 974, 704, 415 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 974, 704, 415 is 1.
HCF(974, 704, 415) = 1
HCF of 974, 704, 415 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 704, 415 is 1.
Highest Common Factor of 974,704,415 is 1
Step 1: Since 974 > 704, we apply the division lemma to 974 and 704, to get
974 = 704 x 1 + 270
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 270 and 704, to get
704 = 270 x 2 + 164
Step 3: We consider the new divisor 270 and the new remainder 164, and apply the division lemma to get
270 = 164 x 1 + 106
We consider the new divisor 164 and the new remainder 106,and apply the division lemma to get
164 = 106 x 1 + 58
We consider the new divisor 106 and the new remainder 58,and apply the division lemma to get
106 = 58 x 1 + 48
We consider the new divisor 58 and the new remainder 48,and apply the division lemma to get
58 = 48 x 1 + 10
We consider the new divisor 48 and the new remainder 10,and apply the division lemma to get
48 = 10 x 4 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 704 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(48,10) = HCF(58,48) = HCF(106,58) = HCF(164,106) = HCF(270,164) = HCF(704,270) = HCF(974,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 415 > 2, we apply the division lemma to 415 and 2, to get
415 = 2 x 207 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 415 is 1
Notice that 1 = HCF(2,1) = HCF(415,2) .
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Frequently Asked Questions on HCF of 974, 704, 415 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 974, 704, 415?
Answer: HCF of 974, 704, 415 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 704, 415 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 704, 415 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
