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 203, 945, 827 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 203, 945, 827 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 203, 945, 827 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 203, 945, 827 is 1.
HCF(203, 945, 827) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 203, 945, 827 is 1.
Step 1: Since 945 > 203, we apply the division lemma to 945 and 203, to get
945 = 203 x 4 + 133
Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 133 and 203, to get
203 = 133 x 1 + 70
Step 3: We consider the new divisor 133 and the new remainder 70, and apply the division lemma to get
133 = 70 x 1 + 63
We consider the new divisor 70 and the new remainder 63,and apply the division lemma to get
70 = 63 x 1 + 7
We consider the new divisor 63 and the new remainder 7,and apply the division lemma to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 203 and 945 is 7
Notice that 7 = HCF(63,7) = HCF(70,63) = HCF(133,70) = HCF(203,133) = HCF(945,203) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 827 > 7, we apply the division lemma to 827 and 7, to get
827 = 7 x 118 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 827 is 1
Notice that 1 = HCF(7,1) = HCF(827,7) .
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 203, 945, 827?
Answer: HCF of 203, 945, 827 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 203, 945, 827 using Euclid's Algorithm?
Answer: For arbitrary numbers 203, 945, 827 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.