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 6705, 1835 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 6705, 1835 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 6705, 1835 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 6705, 1835 is 5.
HCF(6705, 1835) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6705, 1835 is 5.
Step 1: Since 6705 > 1835, we apply the division lemma to 6705 and 1835, to get
6705 = 1835 x 3 + 1200
Step 2: Since the reminder 1835 ≠ 0, we apply division lemma to 1200 and 1835, to get
1835 = 1200 x 1 + 635
Step 3: We consider the new divisor 1200 and the new remainder 635, and apply the division lemma to get
1200 = 635 x 1 + 565
We consider the new divisor 635 and the new remainder 565,and apply the division lemma to get
635 = 565 x 1 + 70
We consider the new divisor 565 and the new remainder 70,and apply the division lemma to get
565 = 70 x 8 + 5
We consider the new divisor 70 and the new remainder 5,and apply the division lemma to get
70 = 5 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6705 and 1835 is 5
Notice that 5 = HCF(70,5) = HCF(565,70) = HCF(635,565) = HCF(1200,635) = HCF(1835,1200) = HCF(6705,1835) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 6705, 1835?
Answer: HCF of 6705, 1835 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6705, 1835 using Euclid's Algorithm?
Answer: For arbitrary numbers 6705, 1835 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.