Highest Common Factor of 369, 969, 348 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 369, 969, 348 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 369, 969, 348 is 3 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 369, 969, 348 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 369, 969, 348 is 3.
HCF(369, 969, 348) = 3
HCF of 369, 969, 348 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 369, 969, 348 is 3.
Highest Common Factor of 369,969,348 is 3
Step 1: Since 969 > 369, we apply the division lemma to 969 and 369, to get
969 = 369 x 2 + 231
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 231 and 369, to get
369 = 231 x 1 + 138
Step 3: We consider the new divisor 231 and the new remainder 138, and apply the division lemma to get
231 = 138 x 1 + 93
We consider the new divisor 138 and the new remainder 93,and apply the division lemma to get
138 = 93 x 1 + 45
We consider the new divisor 93 and the new remainder 45,and apply the division lemma to get
93 = 45 x 2 + 3
We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 369 and 969 is 3
Notice that 3 = HCF(45,3) = HCF(93,45) = HCF(138,93) = HCF(231,138) = HCF(369,231) = HCF(969,369) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 348 > 3, we apply the division lemma to 348 and 3, to get
348 = 3 x 116 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 348 is 3
Notice that 3 = HCF(348,3) .
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Frequently Asked Questions on HCF of 369, 969, 348 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 369, 969, 348?
Answer: HCF of 369, 969, 348 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 369, 969, 348 using Euclid's Algorithm?
Answer: For arbitrary numbers 369, 969, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.