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 619, 968, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 619, 968, 400 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 619, 968, 400 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 619, 968, 400 is 1.
HCF(619, 968, 400) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 619, 968, 400 is 1.
Step 1: Since 968 > 619, we apply the division lemma to 968 and 619, to get
968 = 619 x 1 + 349
Step 2: Since the reminder 619 ≠ 0, we apply division lemma to 349 and 619, to get
619 = 349 x 1 + 270
Step 3: We consider the new divisor 349 and the new remainder 270, and apply the division lemma to get
349 = 270 x 1 + 79
We consider the new divisor 270 and the new remainder 79,and apply the division lemma to get
270 = 79 x 3 + 33
We consider the new divisor 79 and the new remainder 33,and apply the division lemma to get
79 = 33 x 2 + 13
We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get
33 = 13 x 2 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 619 and 968 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(79,33) = HCF(270,79) = HCF(349,270) = HCF(619,349) = HCF(968,619) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 400 > 1, we apply the division lemma to 400 and 1, to get
400 = 1 x 400 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 400 is 1
Notice that 1 = HCF(400,1) .
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 619, 968, 400?
Answer: HCF of 619, 968, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 619, 968, 400 using Euclid's Algorithm?
Answer: For arbitrary numbers 619, 968, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.