Highest Common Factor of 727, 974 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 727, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 727, 974 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 727, 974 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 727, 974 is 1.
HCF(727, 974) = 1
HCF of 727, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 727, 974 is 1.
Highest Common Factor of 727,974 is 1
Step 1: Since 974 > 727, we apply the division lemma to 974 and 727, to get
974 = 727 x 1 + 247
Step 2: Since the reminder 727 ≠ 0, we apply division lemma to 247 and 727, to get
727 = 247 x 2 + 233
Step 3: We consider the new divisor 247 and the new remainder 233, and apply the division lemma to get
247 = 233 x 1 + 14
We consider the new divisor 233 and the new remainder 14,and apply the division lemma to get
233 = 14 x 16 + 9
We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get
14 = 9 x 1 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 727 and 974 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(233,14) = HCF(247,233) = HCF(727,247) = HCF(974,727) .
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Frequently Asked Questions on HCF of 727, 974 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 727, 974?
Answer: HCF of 727, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 727, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 727, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.