Highest Common Factor of 974, 643, 874, 193 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, 643, 874, 193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 643, 874, 193 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, 643, 874, 193 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, 643, 874, 193 is 1.
HCF(974, 643, 874, 193) = 1
HCF of 974, 643, 874, 193 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, 643, 874, 193 is 1.
Highest Common Factor of 974,643,874,193 is 1
Step 1: Since 974 > 643, we apply the division lemma to 974 and 643, to get
974 = 643 x 1 + 331
Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 331 and 643, to get
643 = 331 x 1 + 312
Step 3: We consider the new divisor 331 and the new remainder 312, and apply the division lemma to get
331 = 312 x 1 + 19
We consider the new divisor 312 and the new remainder 19,and apply the division lemma to get
312 = 19 x 16 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 974 and 643 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(312,19) = HCF(331,312) = HCF(643,331) = HCF(974,643) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 1, we apply the division lemma to 874 and 1, to get
874 = 1 x 874 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 874 is 1
Notice that 1 = HCF(874,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 193 > 1, we apply the division lemma to 193 and 1, to get
193 = 1 x 193 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 193 is 1
Notice that 1 = HCF(193,1) .
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Frequently Asked Questions on HCF of 974, 643, 874, 193 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, 643, 874, 193?
Answer: HCF of 974, 643, 874, 193 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 643, 874, 193 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 643, 874, 193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
