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 350, 525, 820 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 350, 525, 820 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 350, 525, 820 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 350, 525, 820 is 5.
HCF(350, 525, 820) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 350, 525, 820 is 5.
Step 1: Since 525 > 350, we apply the division lemma to 525 and 350, to get
525 = 350 x 1 + 175
Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 175 and 350, to get
350 = 175 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 175, the HCF of 350 and 525 is 175
Notice that 175 = HCF(350,175) = HCF(525,350) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 820 > 175, we apply the division lemma to 820 and 175, to get
820 = 175 x 4 + 120
Step 2: Since the reminder 175 ≠ 0, we apply division lemma to 120 and 175, to get
175 = 120 x 1 + 55
Step 3: We consider the new divisor 120 and the new remainder 55, and apply the division lemma to get
120 = 55 x 2 + 10
We consider the new divisor 55 and the new remainder 10,and apply the division lemma to get
55 = 10 x 5 + 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 175 and 820 is 5
Notice that 5 = HCF(10,5) = HCF(55,10) = HCF(120,55) = HCF(175,120) = HCF(820,175) .
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 350, 525, 820?
Answer: HCF of 350, 525, 820 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 350, 525, 820 using Euclid's Algorithm?
Answer: For arbitrary numbers 350, 525, 820 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.