Highest Common Factor of 305, 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 305, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 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 305, 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 305, 969 is 1.
HCF(305, 969) = 1
HCF of 305, 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 305, 969 is 1.
Highest Common Factor of 305,969 is 1
Step 1: Since 969 > 305, we apply the division lemma to 969 and 305, to get
969 = 305 x 3 + 54
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 54 and 305, to get
305 = 54 x 5 + 35
Step 3: We consider the new divisor 54 and the new remainder 35, and apply the division lemma to get
54 = 35 x 1 + 19
We consider the new divisor 35 and the new remainder 19,and apply the division lemma to get
35 = 19 x 1 + 16
We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get
19 = 16 x 1 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 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 305 and 969 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(54,35) = HCF(305,54) = HCF(969,305) .
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Frequently Asked Questions on HCF of 305, 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 305, 969?
Answer: HCF of 305, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.