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 400, 945, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 945, 61 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 400, 945, 61 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 400, 945, 61 is 1.
HCF(400, 945, 61) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 945, 61 is 1.
Step 1: Since 945 > 400, we apply the division lemma to 945 and 400, to get
945 = 400 x 2 + 145
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 145 and 400, to get
400 = 145 x 2 + 110
Step 3: We consider the new divisor 145 and the new remainder 110, and apply the division lemma to get
145 = 110 x 1 + 35
We consider the new divisor 110 and the new remainder 35,and apply the division lemma to get
110 = 35 x 3 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 400 and 945 is 5
Notice that 5 = HCF(35,5) = HCF(110,35) = HCF(145,110) = HCF(400,145) = HCF(945,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 5, we apply the division lemma to 61 and 5, to get
61 = 5 x 12 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 61 is 1
Notice that 1 = HCF(5,1) = HCF(61,5) .
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 400, 945, 61?
Answer: HCF of 400, 945, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 945, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 945, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.