Highest Common Factor of 735, 545, 870 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 735, 545, 870 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 545, 870 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 735, 545, 870 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 735, 545, 870 is 5.
HCF(735, 545, 870) = 5
HCF of 735, 545, 870 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 545, 870 is 5.
Highest Common Factor of 735,545,870 is 5
Step 1: Since 735 > 545, we apply the division lemma to 735 and 545, to get
735 = 545 x 1 + 190
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 190 and 545, to get
545 = 190 x 2 + 165
Step 3: We consider the new divisor 190 and the new remainder 165, and apply the division lemma to get
190 = 165 x 1 + 25
We consider the new divisor 165 and the new remainder 25,and apply the division lemma to get
165 = 25 x 6 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 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 735 and 545 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(165,25) = HCF(190,165) = HCF(545,190) = HCF(735,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 5, we apply the division lemma to 870 and 5, to get
870 = 5 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 870 is 5
Notice that 5 = HCF(870,5) .
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Frequently Asked Questions on HCF of 735, 545, 870 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 735, 545, 870?
Answer: HCF of 735, 545, 870 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 545, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 545, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.