Highest Common Factor of 140, 8505 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 140, 8505 i.e. 35 the largest integer that leaves a remainder zero for all numbers.
HCF of 140, 8505 is 35 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 140, 8505 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 140, 8505 is 35.
HCF(140, 8505) = 35
HCF of 140, 8505 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 140, 8505 is 35.
Highest Common Factor of 140,8505 is 35
Step 1: Since 8505 > 140, we apply the division lemma to 8505 and 140, to get
8505 = 140 x 60 + 105
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 105 and 140, to get
140 = 105 x 1 + 35
Step 3: We consider the new divisor 105 and the new remainder 35, and apply the division lemma to get
105 = 35 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 140 and 8505 is 35
Notice that 35 = HCF(105,35) = HCF(140,105) = HCF(8505,140) .
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Frequently Asked Questions on HCF of 140, 8505 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 140, 8505?
Answer: HCF of 140, 8505 is 35 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 140, 8505 using Euclid's Algorithm?
Answer: For arbitrary numbers 140, 8505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.