Highest Common Factor of 875, 505 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 875, 505 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 875, 505 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 875, 505 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 875, 505 is 5.
HCF(875, 505) = 5
HCF of 875, 505 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 875, 505 is 5.
Highest Common Factor of 875,505 is 5
Step 1: Since 875 > 505, we apply the division lemma to 875 and 505, to get
875 = 505 x 1 + 370
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 370 and 505, to get
505 = 370 x 1 + 135
Step 3: We consider the new divisor 370 and the new remainder 135, and apply the division lemma to get
370 = 135 x 2 + 100
We consider the new divisor 135 and the new remainder 100,and apply the division lemma to get
135 = 100 x 1 + 35
We consider the new divisor 100 and the new remainder 35,and apply the division lemma to get
100 = 35 x 2 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 875 and 505 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(100,35) = HCF(135,100) = HCF(370,135) = HCF(505,370) = HCF(875,505) .
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Frequently Asked Questions on HCF of 875, 505 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 875, 505?
Answer: HCF of 875, 505 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 875, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 875, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.