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, 498 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 498 is 6 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, 498 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, 498 is 6.
HCF(966, 498) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 498 is 6.
Step 1: Since 966 > 498, we apply the division lemma to 966 and 498, to get
966 = 498 x 1 + 468
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 468 and 498, to get
498 = 468 x 1 + 30
Step 3: We consider the new divisor 468 and the new remainder 30, and apply the division lemma to get
468 = 30 x 15 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 966 and 498 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(468,30) = HCF(498,468) = HCF(966,498) .
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, 498?
Answer: HCF of 966, 498 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 498 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.