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 966, 5416 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 5416 is 2 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 966, 5416 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 966, 5416 is 2.
HCF(966, 5416) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 5416 is 2.
Step 1: Since 5416 > 966, we apply the division lemma to 5416 and 966, to get
5416 = 966 x 5 + 586
Step 2: Since the reminder 966 ≠ 0, we apply division lemma to 586 and 966, to get
966 = 586 x 1 + 380
Step 3: We consider the new divisor 586 and the new remainder 380, and apply the division lemma to get
586 = 380 x 1 + 206
We consider the new divisor 380 and the new remainder 206,and apply the division lemma to get
380 = 206 x 1 + 174
We consider the new divisor 206 and the new remainder 174,and apply the division lemma to get
206 = 174 x 1 + 32
We consider the new divisor 174 and the new remainder 32,and apply the division lemma to get
174 = 32 x 5 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 966 and 5416 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(174,32) = HCF(206,174) = HCF(380,206) = HCF(586,380) = HCF(966,586) = HCF(5416,966) .
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 966, 5416?
Answer: HCF of 966, 5416 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 5416 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 5416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.