Highest Common Factor of 535, 8470 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 535, 8470 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 535, 8470 is 5 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 535, 8470 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 535, 8470 is 5.
HCF(535, 8470) = 5
HCF of 535, 8470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 535, 8470 is 5.
Highest Common Factor of 535,8470 is 5
Step 1: Since 8470 > 535, we apply the division lemma to 8470 and 535, to get
8470 = 535 x 15 + 445
Step 2: Since the reminder 535 ≠ 0, we apply division lemma to 445 and 535, to get
535 = 445 x 1 + 90
Step 3: We consider the new divisor 445 and the new remainder 90, and apply the division lemma to get
445 = 90 x 4 + 85
We consider the new divisor 90 and the new remainder 85,and apply the division lemma to get
90 = 85 x 1 + 5
We consider the new divisor 85 and the new remainder 5,and apply the division lemma to get
85 = 5 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 535 and 8470 is 5
Notice that 5 = HCF(85,5) = HCF(90,85) = HCF(445,90) = HCF(535,445) = HCF(8470,535) .
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Frequently Asked Questions on HCF of 535, 8470 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 535, 8470?
Answer: HCF of 535, 8470 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 535, 8470 using Euclid's Algorithm?
Answer: For arbitrary numbers 535, 8470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.