Highest Common Factor of 505, 700, 702 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 505, 700, 702 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 700, 702 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 505, 700, 702 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 505, 700, 702 is 1.
HCF(505, 700, 702) = 1
HCF of 505, 700, 702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 700, 702 is 1.
Highest Common Factor of 505,700,702 is 1
Step 1: Since 700 > 505, we apply the division lemma to 700 and 505, to get
700 = 505 x 1 + 195
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 195 and 505, to get
505 = 195 x 2 + 115
Step 3: We consider the new divisor 195 and the new remainder 115, and apply the division lemma to get
195 = 115 x 1 + 80
We consider the new divisor 115 and the new remainder 80,and apply the division lemma to get
115 = 80 x 1 + 35
We consider the new divisor 80 and the new remainder 35,and apply the division lemma to get
80 = 35 x 2 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 700 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(80,35) = HCF(115,80) = HCF(195,115) = HCF(505,195) = HCF(700,505) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 702 > 5, we apply the division lemma to 702 and 5, to get
702 = 5 x 140 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 702 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(702,5) .
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Frequently Asked Questions on HCF of 505, 700, 702 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 505, 700, 702?
Answer: HCF of 505, 700, 702 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 700, 702 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 700, 702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
