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 435, 680 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 435, 680 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 435, 680 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 435, 680 is 5.
HCF(435, 680) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 435, 680 is 5.
Step 1: Since 680 > 435, we apply the division lemma to 680 and 435, to get
680 = 435 x 1 + 245
Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 245 and 435, to get
435 = 245 x 1 + 190
Step 3: We consider the new divisor 245 and the new remainder 190, and apply the division lemma to get
245 = 190 x 1 + 55
We consider the new divisor 190 and the new remainder 55,and apply the division lemma to get
190 = 55 x 3 + 25
We consider the new divisor 55 and the new remainder 25,and apply the division lemma to get
55 = 25 x 2 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 435 and 680 is 5
Notice that 5 = HCF(25,5) = HCF(55,25) = HCF(190,55) = HCF(245,190) = HCF(435,245) = HCF(680,435) .
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 435, 680?
Answer: HCF of 435, 680 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 435, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 435, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.