Highest Common Factor of 543, 974, 985 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 543, 974, 985 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 974, 985 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 543, 974, 985 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 543, 974, 985 is 1.
HCF(543, 974, 985) = 1
HCF of 543, 974, 985 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 543, 974, 985 is 1.
Highest Common Factor of 543,974,985 is 1
Step 1: Since 974 > 543, we apply the division lemma to 974 and 543, to get
974 = 543 x 1 + 431
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 431 and 543, to get
543 = 431 x 1 + 112
Step 3: We consider the new divisor 431 and the new remainder 112, and apply the division lemma to get
431 = 112 x 3 + 95
We consider the new divisor 112 and the new remainder 95,and apply the division lemma to get
112 = 95 x 1 + 17
We consider the new divisor 95 and the new remainder 17,and apply the division lemma to get
95 = 17 x 5 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 543 and 974 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(95,17) = HCF(112,95) = HCF(431,112) = HCF(543,431) = HCF(974,543) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 985 > 1, we apply the division lemma to 985 and 1, to get
985 = 1 x 985 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 985 is 1
Notice that 1 = HCF(985,1) .
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Frequently Asked Questions on HCF of 543, 974, 985 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 543, 974, 985?
Answer: HCF of 543, 974, 985 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 974, 985 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 974, 985 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.