Highest Common Factor of 700, 270, 712 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 700, 270, 712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 700, 270, 712 is 2 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 700, 270, 712 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 700, 270, 712 is 2.
HCF(700, 270, 712) = 2
HCF of 700, 270, 712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 700, 270, 712 is 2.
Highest Common Factor of 700,270,712 is 2
Step 1: Since 700 > 270, we apply the division lemma to 700 and 270, to get
700 = 270 x 2 + 160
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 160 and 270, to get
270 = 160 x 1 + 110
Step 3: We consider the new divisor 160 and the new remainder 110, and apply the division lemma to get
160 = 110 x 1 + 50
We consider the new divisor 110 and the new remainder 50,and apply the division lemma to get
110 = 50 x 2 + 10
We consider the new divisor 50 and the new remainder 10,and apply the division lemma to get
50 = 10 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 700 and 270 is 10
Notice that 10 = HCF(50,10) = HCF(110,50) = HCF(160,110) = HCF(270,160) = HCF(700,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 712 > 10, we apply the division lemma to 712 and 10, to get
712 = 10 x 71 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, 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 10 and 712 is 2
Notice that 2 = HCF(10,2) = HCF(712,10) .
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Frequently Asked Questions on HCF of 700, 270, 712 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 700, 270, 712?
Answer: HCF of 700, 270, 712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 700, 270, 712 using Euclid's Algorithm?
Answer: For arbitrary numbers 700, 270, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.