Highest Common Factor of 754, 969 using Euclid's algorithm
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 754, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 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 754, 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 754, 969 is 1.
HCF(754, 969) = 1
HCF of 754, 969 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 969 is 1.
Highest Common Factor of 754,969 is 1
Step 1: Since 969 > 754, we apply the division lemma to 969 and 754, to get
969 = 754 x 1 + 215
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 215 and 754, to get
754 = 215 x 3 + 109
Step 3: We consider the new divisor 215 and the new remainder 109, and apply the division lemma to get
215 = 109 x 1 + 106
We consider the new divisor 109 and the new remainder 106,and apply the division lemma to get
109 = 106 x 1 + 3
We consider the new divisor 106 and the new remainder 3,and apply the division lemma to get
106 = 3 x 35 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 754 and 969 is 1
Notice that 1 = HCF(3,1) = HCF(106,3) = HCF(109,106) = HCF(215,109) = HCF(754,215) = HCF(969,754) .
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Frequently Asked Questions on HCF of 754, 969 using Euclid's Algorithm
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 754, 969?
Answer: HCF of 754, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.