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, 602, 196 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 602, 196 is 14 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, 602, 196 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, 602, 196 is 14.
HCF(966, 602, 196) = 14
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 602, 196 is 14.
Step 1: Since 966 > 602, we apply the division lemma to 966 and 602, to get
966 = 602 x 1 + 364
Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 364 and 602, to get
602 = 364 x 1 + 238
Step 3: We consider the new divisor 364 and the new remainder 238, and apply the division lemma to get
364 = 238 x 1 + 126
We consider the new divisor 238 and the new remainder 126,and apply the division lemma to get
238 = 126 x 1 + 112
We consider the new divisor 126 and the new remainder 112,and apply the division lemma to get
126 = 112 x 1 + 14
We consider the new divisor 112 and the new remainder 14,and apply the division lemma to get
112 = 14 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 966 and 602 is 14
Notice that 14 = HCF(112,14) = HCF(126,112) = HCF(238,126) = HCF(364,238) = HCF(602,364) = HCF(966,602) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 196 > 14, we apply the division lemma to 196 and 14, to get
196 = 14 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 196 is 14
Notice that 14 = HCF(196,14) .
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, 602, 196?
Answer: HCF of 966, 602, 196 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 602, 196 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 602, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.