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 825, 195, 761, 512 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 195, 761, 512 is 1 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 825, 195, 761, 512 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 825, 195, 761, 512 is 1.
HCF(825, 195, 761, 512) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 825, 195, 761, 512 is 1.
Step 1: Since 825 > 195, we apply the division lemma to 825 and 195, to get
825 = 195 x 4 + 45
Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 45 and 195, to get
195 = 45 x 4 + 15
Step 3: We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 825 and 195 is 15
Notice that 15 = HCF(45,15) = HCF(195,45) = HCF(825,195) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 761 > 15, we apply the division lemma to 761 and 15, to get
761 = 15 x 50 + 11
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 11 and 15, to get
15 = 11 x 1 + 4
Step 3: We consider the new divisor 11 and the new remainder 4, and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 761 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(761,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 512 > 1, we apply the division lemma to 512 and 1, to get
512 = 1 x 512 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 512 is 1
Notice that 1 = HCF(512,1) .
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 825, 195, 761, 512?
Answer: HCF of 825, 195, 761, 512 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 195, 761, 512 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 195, 761, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.