Highest Common Factor of 506, 597, 972 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 506, 597, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 597, 972 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 506, 597, 972 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 506, 597, 972 is 1.
HCF(506, 597, 972) = 1
HCF of 506, 597, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 597, 972 is 1.
Highest Common Factor of 506,597,972 is 1
Step 1: Since 597 > 506, we apply the division lemma to 597 and 506, to get
597 = 506 x 1 + 91
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 91 and 506, to get
506 = 91 x 5 + 51
Step 3: We consider the new divisor 91 and the new remainder 51, and apply the division lemma to get
91 = 51 x 1 + 40
We consider the new divisor 51 and the new remainder 40,and apply the division lemma to get
51 = 40 x 1 + 11
We consider the new divisor 40 and the new remainder 11,and apply the division lemma to get
40 = 11 x 3 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 506 and 597 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(40,11) = HCF(51,40) = HCF(91,51) = HCF(506,91) = HCF(597,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 1, we apply the division lemma to 972 and 1, to get
972 = 1 x 972 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 972 is 1
Notice that 1 = HCF(972,1) .
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Frequently Asked Questions on HCF of 506, 597, 972 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 506, 597, 972?
Answer: HCF of 506, 597, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 597, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 597, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
