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 590, 710, 356, 701 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 590, 710, 356, 701 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 590, 710, 356, 701 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 590, 710, 356, 701 is 1.
HCF(590, 710, 356, 701) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 590, 710, 356, 701 is 1.
Step 1: Since 710 > 590, we apply the division lemma to 710 and 590, to get
710 = 590 x 1 + 120
Step 2: Since the reminder 590 ≠ 0, we apply division lemma to 120 and 590, to get
590 = 120 x 4 + 110
Step 3: We consider the new divisor 120 and the new remainder 110, and apply the division lemma to get
120 = 110 x 1 + 10
We consider the new divisor 110 and the new remainder 10, and apply the division lemma to get
110 = 10 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 590 and 710 is 10
Notice that 10 = HCF(110,10) = HCF(120,110) = HCF(590,120) = HCF(710,590) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 356 > 10, we apply the division lemma to 356 and 10, to get
356 = 10 x 35 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: 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 10 and 356 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(356,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 701 > 2, we apply the division lemma to 701 and 2, to get
701 = 2 x 350 + 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 701 is 1
Notice that 1 = HCF(2,1) = HCF(701,2) .
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 590, 710, 356, 701?
Answer: HCF of 590, 710, 356, 701 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 590, 710, 356, 701 using Euclid's Algorithm?
Answer: For arbitrary numbers 590, 710, 356, 701 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.