Highest Common Factor of 528, 706, 172, 39 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 528, 706, 172, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 528, 706, 172, 39 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 528, 706, 172, 39 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 528, 706, 172, 39 is 1.
HCF(528, 706, 172, 39) = 1
HCF of 528, 706, 172, 39 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 528, 706, 172, 39 is 1.
Highest Common Factor of 528,706,172,39 is 1
Step 1: Since 706 > 528, we apply the division lemma to 706 and 528, to get
706 = 528 x 1 + 178
Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 178 and 528, to get
528 = 178 x 2 + 172
Step 3: We consider the new divisor 178 and the new remainder 172, and apply the division lemma to get
178 = 172 x 1 + 6
We consider the new divisor 172 and the new remainder 6,and apply the division lemma to get
172 = 6 x 28 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 528 and 706 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(172,6) = HCF(178,172) = HCF(528,178) = HCF(706,528) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 2, we apply the division lemma to 172 and 2, to get
172 = 2 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 172 is 2
Notice that 2 = HCF(172,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39 > 2, we apply the division lemma to 39 and 2, to get
39 = 2 x 19 + 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 39 is 1
Notice that 1 = HCF(2,1) = HCF(39,2) .
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Frequently Asked Questions on HCF of 528, 706, 172, 39 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 528, 706, 172, 39?
Answer: HCF of 528, 706, 172, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 528, 706, 172, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 528, 706, 172, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.