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, 590, 503 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 590, 503 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, 590, 503 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, 590, 503 is 1.
HCF(974, 590, 503) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 590, 503 is 1.
Step 1: Since 974 > 590, we apply the division lemma to 974 and 590, to get
974 = 590 x 1 + 384
Step 2: Since the reminder 590 ≠ 0, we apply division lemma to 384 and 590, to get
590 = 384 x 1 + 206
Step 3: We consider the new divisor 384 and the new remainder 206, and apply the division lemma to get
384 = 206 x 1 + 178
We consider the new divisor 206 and the new remainder 178,and apply the division lemma to get
206 = 178 x 1 + 28
We consider the new divisor 178 and the new remainder 28,and apply the division lemma to get
178 = 28 x 6 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 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 590 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(178,28) = HCF(206,178) = HCF(384,206) = HCF(590,384) = HCF(974,590) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 503 > 2, we apply the division lemma to 503 and 2, to get
503 = 2 x 251 + 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 503 is 1
Notice that 1 = HCF(2,1) = HCF(503,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 590, 503?
Answer: HCF of 974, 590, 503 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 590, 503 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 590, 503 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.