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 974, 664, 97 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 664, 97 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 974, 664, 97 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 974, 664, 97 is 1.
HCF(974, 664, 97) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 664, 97 is 1.
Step 1: Since 974 > 664, we apply the division lemma to 974 and 664, to get
974 = 664 x 1 + 310
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 310 and 664, to get
664 = 310 x 2 + 44
Step 3: We consider the new divisor 310 and the new remainder 44, and apply the division lemma to get
310 = 44 x 7 + 2
We consider the new divisor 44 and the new remainder 2, and apply the division lemma to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 664 is 2
Notice that 2 = HCF(44,2) = HCF(310,44) = HCF(664,310) = HCF(974,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97 > 2, we apply the division lemma to 97 and 2, to get
97 = 2 x 48 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 97 is 1
Notice that 1 = HCF(2,1) = HCF(97,2) .
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 974, 664, 97?
Answer: HCF of 974, 664, 97 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 664, 97 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 664, 97 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.