Highest Common Factor of 310, 434, 535 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 310, 434, 535 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 434, 535 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 310, 434, 535 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 310, 434, 535 is 1.
HCF(310, 434, 535) = 1
HCF of 310, 434, 535 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 434, 535 is 1.
Highest Common Factor of 310,434,535 is 1
Step 1: Since 434 > 310, we apply the division lemma to 434 and 310, to get
434 = 310 x 1 + 124
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 124 and 310, to get
310 = 124 x 2 + 62
Step 3: We consider the new divisor 124 and the new remainder 62, and apply the division lemma to get
124 = 62 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 62, the HCF of 310 and 434 is 62
Notice that 62 = HCF(124,62) = HCF(310,124) = HCF(434,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 535 > 62, we apply the division lemma to 535 and 62, to get
535 = 62 x 8 + 39
Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 39 and 62, to get
62 = 39 x 1 + 23
Step 3: We consider the new divisor 39 and the new remainder 23, and apply the division lemma to get
39 = 23 x 1 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
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 62 and 535 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(39,23) = HCF(62,39) = HCF(535,62) .
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Frequently Asked Questions on HCF of 310, 434, 535 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 310, 434, 535?
Answer: HCF of 310, 434, 535 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 434, 535 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 434, 535 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.