Highest Common Factor of 400, 945, 978, 879 using Euclid's algorithm
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, 978, 879 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 945, 978, 879 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, 978, 879 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, 978, 879 is 1.
HCF(400, 945, 978, 879) = 1
HCF of 400, 945, 978, 879 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 945, 978, 879 is 1.
Highest Common Factor of 400,945,978,879 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 978 > 5, we apply the division lemma to 978 and 5, to get
978 = 5 x 195 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 978 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(978,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 879 > 1, we apply the division lemma to 879 and 1, to get
879 = 1 x 879 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 879 is 1
Notice that 1 = HCF(879,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 400, 945, 978, 879 using Euclid's Algorithm
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, 978, 879?
Answer: HCF of 400, 945, 978, 879 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 945, 978, 879 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 945, 978, 879 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.