Highest Common Factor of 722, 524, 59 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 722, 524, 59 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 524, 59 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 722, 524, 59 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 722, 524, 59 is 1.
HCF(722, 524, 59) = 1
HCF of 722, 524, 59 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 524, 59 is 1.
Highest Common Factor of 722,524,59 is 1
Step 1: Since 722 > 524, we apply the division lemma to 722 and 524, to get
722 = 524 x 1 + 198
Step 2: Since the reminder 524 ≠ 0, we apply division lemma to 198 and 524, to get
524 = 198 x 2 + 128
Step 3: We consider the new divisor 198 and the new remainder 128, and apply the division lemma to get
198 = 128 x 1 + 70
We consider the new divisor 128 and the new remainder 70,and apply the division lemma to get
128 = 70 x 1 + 58
We consider the new divisor 70 and the new remainder 58,and apply the division lemma to get
70 = 58 x 1 + 12
We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 722 and 524 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(128,70) = HCF(198,128) = HCF(524,198) = HCF(722,524) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 59 > 2, we apply the division lemma to 59 and 2, to get
59 = 2 x 29 + 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 59 is 1
Notice that 1 = HCF(2,1) = HCF(59,2) .
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Frequently Asked Questions on HCF of 722, 524, 59 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 722, 524, 59?
Answer: HCF of 722, 524, 59 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 524, 59 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 524, 59 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.