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 645, 749, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 749, 969 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 645, 749, 969 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 645, 749, 969 is 1.
HCF(645, 749, 969) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 749, 969 is 1.
Step 1: Since 749 > 645, we apply the division lemma to 749 and 645, to get
749 = 645 x 1 + 104
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 104 and 645, to get
645 = 104 x 6 + 21
Step 3: We consider the new divisor 104 and the new remainder 21, and apply the division lemma to get
104 = 21 x 4 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 645 and 749 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(104,21) = HCF(645,104) = HCF(749,645) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 969 > 1, we apply the division lemma to 969 and 1, to get
969 = 1 x 969 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 969 is 1
Notice that 1 = HCF(969,1) .
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 645, 749, 969?
Answer: HCF of 645, 749, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 749, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 749, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.